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 | Q16 | S5 |
| hypocenter | SL(2,𝔽5) | D8 |
| LCS | G ▷ #91145 ▷ #6732 ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ Q16 | |
166 conjugacy classes of subgroups; only the 12 normal subgroups are shown.
This group has 166 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:
(1,63,32,53,17,52,16,49,6,80,15,65,5,64,4,54)(2,89,45,76,24,79,44,78,10,74,33,73,9,61,48,60)(3,67,19,83,27,95,47,82,14,85,37,66,11,84,36,94)(7,92,31,86,38,81,26,69,21,96,13,68,20,93,41,55)(8,51,46,90,39,75,35,91,23,62,34,88,22,59,18,77)(12,70,40,72,28,56,29,58,30,87,42,57,25,71,43,50)(97,151,109,175,101,164,122,185,102,165,127,157,113,182,137,170)(98,169,133,160,105,174,143,176,106,172,115,148,120,156,132,159)(99,158,100,163,107,171,111,180,110,147,112,181,123,155,128,191)(103,145,119,186,116,149,135,173,117,150,104,184,134,161,118,187)(108,168,125,183,121,146,136,152,126,153,139,166,124,154,138,167)(114,162,141,189,130,178,144,192,131,179,129,177,142,190,140,188);(1,139,24,140,28,122,6,125,9,144,25,137)(2,141,12,127,17,136,10,129,30,109,5,138)(3,112,21,104,46,132,14,100,7,119,34,143)(4,124,39,131,42,110,16,121,22,114,40,99)(8,142,29,123,32,126,23,130,43,107,15,108)(11,128,38,118,18,133,27,111,20,135,35,115)(13,113,37,105,48,117,31,101,19,120,44,103)(26,97,47,106,33,134,41,102,36,98,45,116)(49,183,68,189,50,173,54,166,86,177,58,187)(51,181,66,185,73,148,62,163,83,170,76,160)(52,146,84,190,56,169,64,154,95,178,71,172)(53,152,69,192,57,184,65,167,55,188,72,186)(59,191,82,157,78,159,75,180,94,175,60,176)(61,182,81,147,88,149,79,164,93,158,90,161)(63,153,85,162,70,174,80,168,67,179,87,156)(74,151,92,155,91,150,89,165,96,171,77,145)36 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240711);