Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | C2×C4⋊S5 |
| commutator, cosocle | #6732 | C23 |
| Frattini | C4 | C22×S5 |
| Fitting, hypercenter | M16 | S5 |
| hypocenter | SL(2,𝔽5) | C2×D4 |
| LCS | G ▷ #6732 ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ M16 | |
450 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 28 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 80 |
| transitive degree | μt(G) = 80 |
Permutation generators:
(1,21,12,79,68,55,7,28,15,65,49,61,37,30,3,70,16,58,50,76,9,29,14,80,67,60,6,23,20,66,51,53,33,25,8,72,17,59,52,75)(2,48,18,71,32,44,34,22,5,41,19,56,77,42,35,26,74,47,63,62,4,43,13,69,31,45,36,24,10,46,11,54,78,40,38,27,73,39,64,57)(81,109,92,160,148,140,87,103,95,146,129,133,117,105,83,152,96,139,130,155,89,101,94,159,147,135,86,108,100,145,131,141,113,110,88,150,97,138,132,156)(82,123,98,149,112,125,114,104,85,126,99,134,157,120,115,107,154,119,143,137,84,128,93,151,111,124,116,102,90,121,91,136,158,122,118,106,153,127,144,142);(1,73,68,14,9,74,67,12)(2,78,19,13,4,77,11,18)(3,37,51,34,8,33,49,36)(5,20,17,32,10,15,16,31)(6,35,63,50,7,38,64,52)(21,62,40,80,29,57,42,79)(22,26,39,45,24,27,47,44)(23,72,43,75,28,70,48,76)(25,61,41,71,30,53,46,69)(54,66,58,55,56,65,59,60)(81,153,148,94,89,154,147,92)(82,158,99,93,84,157,91,98)(83,117,131,114,88,113,129,116)(85,100,97,112,90,95,96,111)(86,115,143,130,87,118,144,132)(101,142,120,160,109,137,122,159)(102,106,119,125,104,107,127,124)(103,152,123,155,108,150,128,156)(105,141,121,151,110,133,126,149)(134,146,138,135,136,145,139,140);(1,81)(2,82)(3,83)(4,84)(5,85)(6,86)(7,87)(8,88)(9,89)(10,90)(11,91)(12,92)(13,93)(14,94)(15,95)(16,96)(17,97)(18,98)(19,99)(20,100)(21,101)(22,102)(23,103)(24,104)(25,105)(26,106)(27,107)(28,108)(29,109)(30,110)(31,111)(32,112)(33,113)(34,114)(35,115)(36,116)(37,117)(38,118)(39,119)(40,120)(41,121)(42,122)(43,123)(44,124)(45,125)(46,126)(47,127)(48,128)(49,129)(50,130)(51,131)(52,132)(53,133)(54,134)(55,135)(56,136)(57,137)(58,138)(59,139)(60,140)(61,141)(62,142)(63,143)(64,144)(65,145)(66,146)(67,147)(68,148)(69,149)(70,150)(71,151)(72,152)(73,153)(74,154)(75,155)(76,156)(77,157)(78,158)(79,159)(80,160)42 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240834);