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 | #11751487 |
| commutator, cosocle | #91145 | C22 |
| Frattini | C8 | C2×S5 |
| Fitting, hypercenter | C16 | S5 |
| hypocenter | SL(2,𝔽5) | D8 |
| LCS | G ▷ #91145 ▷ #6732 ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 | |
154 conjugacy classes of subgroups; only the 12 normal subgroups are shown.
This group has 154 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:
(1,92,68,55,12,75,80,67,27,60,49,78,38,54,32,48,53,74,26,30,23,91,45,25,11,47,79,44,8,29,22,77,17,95,10,20,52,66,85,9,7,76,37,84,2,46,51,36,59,86,21,50,13,83,63,19,24,43,58,62,6,96,16,56,34,18,94,15,28,61,5,93,3,82,33,4,81,88,57,31)(14,71,65,72,39,89,41,64,42,90,70,40,35,87,73,69)(97,160,159,178,149,100,161,182,124,174,101,183,98,152,176,114,138,105,154,188,102,168,106,179,177,115,169,125,155,189,117,186,107,180,190,142,135,126,181,192,103,165,128,191,120,116,166,156,104,146,118,185,108,121,147,143,110,127,122,172,119,136,129,150,148,144,137,157,123,173,145,167,130,151,175,171,131,158,153,187)(99,163,141,162,109,111,164,170,113,132,112,184,134,140,133,139);(1,174,6,189,7,146,23,173)(2,126,13,111,12,158,38,140)(3,163,11,127,17,132,34,105)(4,176,19,190,20,147,48,175)(5,188,21,192,22,172,49,187)(8,165,42,151,28,160,14,180)(9,128,36,112,31,159,67,141)(10,156,37,139,33,182,68,170)(15,164,30,129,44,133,62,106)(16,184,32,157,45,162,63,125)(18,177,46,120,47,148,75,149)(24,100,81,144,53,116,52,115)(25,166,72,153,56,161,40,181)(26,185,73,178,58,183,41,191)(27,136,39,152,59,168,35,121)(29,108,66,109,61,98,88,134)(43,99,60,130,74,113,86,107)(50,101,93,145,78,118,77,117)(51,114,94,171,80,143,79,142)(54,110,90,124,83,138,71,104)(55,137,69,154,84,169,64,122)(57,167,70,179,85,186,65,150)(76,102,96,97,92,119,91,103)(82,131,89,155,95,135,87,123)45 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240715);