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 | C22 | C22×S5 |
| commutator, cosocle | C2×SL(2,𝔽5) | C23 |
| Fitting, hypercenter | C22⋊C4 | S5 |
| hypocenter | SL(2,𝔽5) | C2×D4 |
| LCS | G ▷ C2×SL(2,𝔽5) ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C22 ◁ C22⋊C4 | |
461 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 461 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.
| transitive degree | μt(G) = 192 |
Permutation generators:
(1,4,2,3)(5,44,6,43)(7,11,8,12)(9,29,10,30)(13,20,14,19)(15,24,16,23)(17,22,18,21)(25,40,26,39)(27,36,28,35)(31,50,32,49)(33,37,34,38)(41,52,42,51)(45,47,46,48)(53,55,54,56)(57,95,58,96)(59,64,60,63)(61,82,62,81)(65,71,66,72)(67,75,68,76)(69,73,70,74)(77,91,78,92)(79,87,80,88)(83,101,84,102)(85,90,86,89)(93,103,94,104)(97,100,98,99);(1,4)(2,3)(5,28,12,42,6,27,11,41)(7,46,25,35,8,45,26,36)(9,37,24,13,10,38,23,14)(15,52,18,48,16,51,17,47)(19,39,31,43,20,40,32,44)(21,49,30,34,22,50,29,33)(53,56)(54,55)(57,80,64,94,58,79,63,93)(59,98,77,87,60,97,78,88)(61,89,76,65,62,90,75,66)(67,104,70,100,68,103,69,99)(71,91,83,95,72,92,84,96)(73,101,82,86,74,102,81,85);(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)48 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240839);