Sporadic Group/Catalog

== Catalog of Sporadic Groups ==
The sporadic groups are as follows:
| align="left" | Mathieu Group
| align="center" | $\mathrm M_{11}$
| align="left" | $2^4 \times 3^2 \times 5 \times 11$
| align="center" | $1861$
| align="left" | 
| align="left" | Mathieu Group
| align="center" | $\mathrm M_{12}$
| align="left" | $2^6 \times 3^3 \times 5 \times 11$
| align="center" | $1861$
| align="left" | 
| align="left" | Mathieu Group
| align="center" | $\mathrm M_{22}$
| align="left" | $2^7 \times 3^2 \times 5 \times 7 \times 11$
| align="center" | $1873$
| align="left" | 
| align="left" | Mathieu Group
| align="center" | $\mathrm M_{23}$
| align="left" | $2^7 \times 3^2 \times 5 \times 7 \times 11 \times 23$
| align="center" | $1873$
| align="left" | 
| align="left" | Mathieu Group
| align="center" | $\mathrm M_{24}$
| align="left" | $2^{10} \times 3^3 \times 5 \times 7 \times 11 \times 23$
| align="center" | $1873$
| align="left" | 
| align="left" | Janko Group
| align="center" | $\mathrm J_1$
| align="left" | $2^3 \times 3 \times 5 \times 7 \times 11 \times 19$
| align="center" | $1966$
| align="left" | 
| align="left" | Janko Group
| align="center" | $\mathrm J_2$
| align="left" | $2^7 \times 3^3 \times 5^2 \times 7$
| align="center" | $1968$
| align="left" | 
| align="left" | Janko Group
| align="center" | $\mathrm J_3$
| align="left" | $2^7 \times 3^5 \times 5 \times 17 \times 19$
| align="center" | $1968$
| align="left" | 
| align="left" | Janko Group
| align="center" | $\mathrm J_4$
| align="left" | $2^{21} \times 3^3 \times 5 \times 7 \times 11^3 \times 23 \times 29 \times 31 \times 37 \times 43$
| align="center" | $1976$
| align="left" | 
| align="left" | Higman-Sims Group
| align="center" | $\mathrm {HS}$
| align="left" | $2^9 \times 3^2 \times 5^3 \times 7 \times 11$
| align="center" | $1968$
| align="left" | 
| align="left" | McLaughlin Group
| align="center" | $\mathrm {McL}$
| align="left" | $2^7 \times 3^6 \times 5^3 \times 7 \times 11$
| align="center" | $1969$
| align="left" | 
| align="left" | Suzuki Group
| align="center" | $\mathrm {Suz}$
| align="left" | $2^{13} \times 3^7 \times 5^2 \times 7 \times 11 \times 13$
| align="center" | $1969$
| align="left" | 
| align="left" | Rudvalis Group
| align="center" | $\mathrm {Ru}$
| align="left" | $2^{14} \times 3^3 \times 5^3 \times 7 \times 13 \times 29$
| align="center" | $1973$
| align="left" | 
| align="left" | Held Group
| align="center" | $\mathrm {He}$
| align="left" | $2^{10} \times 3^2 \times 5^2 \times 7^3 \times 17$
| align="center" | $1969$
| align="left" | 
| align="left" | Lyons Group
| align="center" | $\mathrm {Ly}$
| align="left" | $2^8 \times 3^7 \times 5^6 \times 7 \times 11 \times 31 \times 37 \times 67$
| align="center" | $1972$
| align="left" | 
| align="left" | O'Nan Group
| align="center" | $\text {O'N}$
| align="left" | $2^9 \times 3^4 \times 5 \times 7^3 \times 11 \times 19 \times 31$
| align="center" | $1976$
| align="left" | 
| align="left" | Conway Group
| align="center" | $\mathrm {Co3}$
| align="left" | $2^{10} \times 3^7 \times 5^3 \times 7 \times 11 \times 23$
| align="center" | $1969$
| align="left" | 
| align="left" | Conway Group
| align="center" | $\mathrm {Co2}$
| align="left" | $2^{18} \times 3^6 \times 5^3 \times 7 \times 11 \times 23$
| align="center" | $1969$
| align="left" | 
| align="left" | Conway Group
| align="center" | $\mathrm {Co1}$
| align="left" | $2^{21} \times 3^9 \times 5^4 \times 7^2 \times 11 \times 13 \times 23$
| align="center" | $1969$
| align="left" | 
| align="left" | Fischer Group
| align="center" | $\map {\mathrm {Fi} } {22}$
| align="left" | $2^{17} \times 3^9 \times 5^2 \times 7 \times 11 \times 13$
| align="center" | $1971$
| align="left" | 
| align="left" | Fischer Group
| align="center" | $\map {\mathrm {Fi} } {23}$
| align="left" | $2^{18} \times 3^{13} \times 5^2 \times 7 \times 11 \times 13 \times 17 \times 23$
| align="center" | $1971$
| align="left" | 
| align="left" | Fischer Group
| align="center" | ${\map {\mathrm {Fi} } {24} }'$
| align="left" | $2^{21} \times 3^{16} \times 5^2 \times 7^3 \times 11 \times 13 \times 17 \times 23 \times 29$
| align="center" | $1971$
| align="left" | 
| align="left" | Harada-Norton Group
| align="center" | $\mathrm {HN}$
| align="left" | $2^{14} \times 3^6 \times 5^6 \times 7 \times 11 \times 19$
| align="center" | $1976$
| align="left" | 
| align="left" | Thompson Group
| align="center" | $\mathrm {Th}$
| align="left" | $2^{15} \times 3^{10} \times 5^3 \times 7^2 \times 13 \times 19 \times 31$
| align="center" | $1976$
| align="left" | 
| align="left" | Baby Monster
| align="center" | $\mathrm {BM}$
| align="left" | $2^{41} \times 3^{13} \times 5^6 \times 7^2 \times 11 \times 13 \times 17 \times 19 \times 23 \times 31 \times 47$
| align="center" | $1976$
| align="left" | 
| align="left" | Fischer-Griess Monster
| align="center" | $\mathrm {M}$
| align="left" | $2^{46} \times 3^{20} \times 5^9 \times 7^6 \times 11^2 \times 13^3 \times 17 \times 19 \times 23 \times 29 \times 31 \times 41 \times 47 \times 59 \times 71$
| align="center" | $1981$
| align="left" | 
== Sources ==
* : $\S 25.3$: The Sporadic Groups
Category:Sporadic Groups