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, Frattini, socle, cosocle | C22 | C23×A5 |
| commutator | C2×SL(2,𝔽5) | C23 |
| Fitting, hypercenter | #123 | A5 |
| hypocenter | SL(2,𝔽5) | C2×D4 |
| LCS | G ▷ C2×SL(2,𝔽5) ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C22 ◁ #123 | |
684 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 41 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
Permutation generators:
(1,3,2,4)(5,17,6,18)(7,19,8,20)(9,30,47,24,49,25,13,37,44,34,10,29,48,23,50,26,14,38,43,33)(11,32,45,21,52,27,15,40,41,35,12,31,46,22,51,28,16,39,42,36)(53,56,54,55)(57,69,58,70)(59,71,60,72)(61,82,99,76,101,77,65,89,96,86,62,81,100,75,102,78,66,90,95,85)(63,84,97,73,104,79,67,92,93,87,64,83,98,74,103,80,68,91,94,88);(1,4,2,3)(5,13,36,20,32,49)(6,14,35,19,31,50)(7,16,34,18,29,51)(8,15,33,17,30,52)(9,45,23,28,38,42)(10,46,24,27,37,41)(11,48,21,26,40,44)(12,47,22,25,39,43)(53,55,54,56)(57,65,88,72,84,101)(58,66,87,71,83,102)(59,68,86,70,81,103)(60,67,85,69,82,104)(61,97,75,80,90,94)(62,98,76,79,89,93)(63,100,73,78,92,96)(64,99,74,77,91,95);(1,53)(2,54)(3,55)(4,56)(5,57,6,58)(7,59,8,60)(9,61,10,62)(11,63,12,64)(13,65,14,66)(15,67,16,68)(17,69,18,70)(19,71,20,72)(21,73,22,74)(23,75,24,76)(25,77,26,78)(27,79,28,80)(29,81,30,82)(31,83,32,84)(33,85,34,86)(35,87,36,88)(37,89,38,90)(39,91,40,92)(41,93,42,94)(43,95,44,96)(45,97,46,98)(47,99,48,100)(49,101,50,102)(51,103,52,104)66 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240871);