List of Finite Simple Groups - Non-cyclic Simple Groups of Small Order

Non-cyclic Simple Groups of Small Order

Order Factorized order Group Schur multiplier Outer automorphism group
60 22 · 3 · 5 A5 = A1(4) = A1(5) 2 2
168 23 · 3 · 7 A1(7) = A2(2) 2 2
360 23 · 32 · 5 A6 = A1(9) = B2(2)′ 6 2×2
504 23 · 32 · 7 A1(8) = 2G2(3)′ 1 3
660 22 · 3 · 5 · 11 A1(11) 2 2
1092 22 · 3 · 7 · 13 A1(13) 2 2
2448 24 · 32 · 17 A1(17) 2 2
2520 23 · 32 · 5 · 7 A7 6 2
3420 22 · 32 · 5 · 19 A1(19) 2 2
4080 24 · 3 · 5 · 17 A1(16) 1 4
5616 24 · 33 · 13 A2(3) 1 2
6048 25 · 33 · 7 2A2(9) = G2(2)′ 1 2
6072 23 · 3 · 11 · 23 A1(23) 2 2
7800 23 · 3 · 52 · 13 A1(25) 2 2×2
7920 24 · 32 · 5 · 11 M11 1 1
9828 22 · 33 · 7 · 13 A1(27) 2 6
12180 22 · 3 · 5 · 7 · 29 A1(29) 2 2
14880 25 · 3 · 5 · 31 A1(31) 2 2
20160 26 · 32 · 5 · 7 A3(2) = A8 2 2
20160 26 · 32 · 5 · 7 A2(4) 3×42 D12
25308 22 · 32 · 19 · 37 A1(37) 2 2
25920 26 · 34 · 5 2A3(4) = B2(3) 2 2
29120 26 · 5 · 7 · 13 2B2(8) 22 3
32736 25 · 3 · 11 · 31 A1(32) 1 5
34440 23 · 3 · 5 · 7 · 41 A1(41) 2 2
39732 22 · 3 · 7 · 11 · 43 A1(43) 2 2
51888 24 · 3 · 23 · 47 A1(47) 2 2
58800 24 · 3 · 52 · 72 A1(49) 2 22
62400 26 · 3 · 52 · 13 2A2(16) 1 4
74412 22 · 33 · 13 · 53 A1(53) 2 2
95040 26 · 33 · 5 · 11 M12 2 2

(Complete for orders less than 100,000)

Hall (1972) lists the 56 non-cyclic simple groups of order less than a million.

Read more about this topic:  List Of Finite Simple Groups

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