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 | |
476 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 32 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)(53,56,54,55)(57,96,58,95)(59,63,60,64)(61,81,62,82)(65,72,66,71)(67,76,68,75)(69,74,70,73)(77,92,78,91)(79,88,80,87)(83,102,84,101)(85,89,86,90)(93,104,94,103)(97,99,98,100);(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)(53,55)(54,56)(57,79,64,93,58,80,63,94)(59,97,77,88,60,98,78,87)(61,90,76,66,62,89,75,65)(67,103,70,99,68,104,69,100)(71,92,83,96,72,91,84,95)(73,102,82,85,74,101,81,86);(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)54 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240822);