Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C2×S5 |
| commutator, hypocenter | SL(2,𝔽5) | C2×C8 |
| Fitting, hypercenter | C16 | S5 |
| socle | C2 | C8×S5 |
| prime radical | #91870 | C4 |
| cosocle | #91145 | C22 |
| LCS | G ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C8 ◁ C16 | |
152 conjugacy classes of subgroups; only the 16 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 16 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 96 |
| transitive degree | μt(G) = 96 |
Permutation generators:
(1,126,39,133,35,101,40,104,21,142,4,139,2,134,45,111,30,105,37,144,5,124,8,143,46,102,43,118,38,114,15,138,9,103,48,112,28,106,47,129,6,108,22,115,18,113,42,119,7,130,16,125,10,116,33,128,12,120,19,140,17,121,23,132,34,97,29,135,20,131,32,136,24,117,44,100,25,98,36,141)(3,99,31,127,11,107,41,137,14,110,13,109,27,123,26,122)(49,168,84,157,94,149,71,181,51,162,52,183,69,155,96,159,72,182,61,177,53,146,85,170,66,150,87,191,59,178,63,152,86,158,81,160,50,151,74,188,54,153,95,175,82,161,56,163,62,179,64,166,55,171,92,176,57,164,79,189,65,154,67,185,83,145,70,180,75,190,80,167,68,147,93,148,58,165,89,192)(60,156,91,187,73,169,90,186,78,174,77,173,76,172,88,184);(1,162,7,154,11,151,6,179,21,146,27,165)(2,161,46,155,25,172,10,149,34,171,28,169)(3,182,5,178,20,168,14,164,17,190,38,153)(4,177,19,167,26,163,16,189,37,152,41,181)(8,176,48,170,40,186,23,159,44,185,42,184)(9,145,18,158,30,156,24,150,35,147,12,174)(13,191,15,188,36,183,31,180,32,192,47,166)(22,148,33,175,43,173,39,160,45,157,29,187)(49,144,62,136,60,119,54,140,51,138,78,104)(50,127,69,128,66,143,58,109,55,111,83,132)(52,114,79,126,77,120,64,131,61,108,91,105)(53,129,75,139,73,135,65,141,59,125,76,118)(56,123,85,97,81,103,71,107,67,102,93,117)(57,137,86,100,82,115,72,122,68,112,94,133)(63,130,89,124,88,98,80,142,74,121,90,106)(70,99,95,101,92,116,87,110,84,113,96,134)72 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240685);