Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | #11751518 |
| commutator, cosocle | #91145 | C22 |
| Frattini | C8 | C2×S5 |
| Fitting, hypercenter | D8 | S5 |
| hypocenter | SL(2,𝔽5) | D8 |
| LCS | G ▷ #91145 ▷ #6732 ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ D8 | |
165 conjugacy classes of subgroups; only the 12 normal subgroups are shown.
This group has 165 conjugacy classes of subgroups — too many to draw. Only its 12 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 160 |
| transitive degree | μt(G) = 160 |
Permutation generators:
(1,70,31,59,18,95,15,72,3,79,44,68,17,56,26,51,46,85,4,58,27,74,33,55,6,87,13,75,35,84,32,57,14,61,48,86,5,71,41,62,34,67,16,50,11,89,45,69)(2,80,29,73,38,81,22,53,30,91,19,83,24,64,42,60,21,96,8,49,25,88,47,82,10,63,43,76,20,93,39,65,12,77,37,66,9,52,40,78,7,92,23,54,28,90,36,94)(97,169,129,166,105,158,112,186,142,146,135,157,101,174,140,167,106,171,128,173,114,153,104,170,102,172,141,183,120,147,100,184,130,154,118,175,113,156,144,152,98,155,111,187,131,168,119,185)(99,190,139,163,117,145,127,188,121,182,115,160,107,162,138,180,134,149,137,189,126,151,132,176,110,178,125,181,103,150,109,192,124,164,133,148,123,179,136,191,116,161,122,177,108,165,143,159);(1,164,7,172,35,168)(2,145,28,190,11,158)(3,155,24,161,30,179)(4,180,19,186,45,183)(5,165,20,156,46,146)(6,182,21,169,18,153)(8,148,42,192,26,175)(9,149,12,162,14,171)(10,150,25,178,27,147)(13,170,39,176,43,189)(15,181,36,173,48,152)(16,191,37,184,33,166)(17,151,38,174,34,154)(22,159,29,177,31,185)(23,160,40,188,41,157)(32,163,47,187,44,167)(49,135,62,109,94,139)(50,141,60,115,69,100)(51,127,82,125,54,118)(52,98,79,107,96,124)(53,104,75,122,66,138)(55,112,58,129,78,133)(56,142,77,116,85,101)(57,144,73,132,86,111)(59,137,83,136,65,119)(61,123,92,121,64,106)(63,105,89,110,81,108)(67,113,71,130,91,134)(68,128,72,140,76,143)(70,114,88,117,95,102)(74,99,93,126,80,120)(84,97,87,131,90,103)36 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240712);