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 | |
559 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 559 conjugacy classes of subgroups — too many to draw. Only its 30 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)(5,17,44,50,6,18,43,49)(7,41,45,12,8,42,46,11)(9,32,24,39,10,31,23,40)(13,29,16,27,14,30,15,28)(19,26,36,21,20,25,35,22)(33,51,38,47,34,52,37,48)(53,55)(54,56)(57,70,96,101,58,69,95,102)(59,94,97,63,60,93,98,64)(61,83,76,92,62,84,75,91)(65,82,68,80,66,81,67,79)(71,77,88,74,72,78,87,73)(85,104,90,100,86,103,89,99);(1,3,2,4)(5,52,14,46,19,23,6,51,13,45,20,24)(7,44,21,33,30,39,8,43,22,34,29,40)(9,37,28,36,17,42,10,38,27,35,18,41)(11,47,15,50,31,25,12,48,16,49,32,26)(53,55,54,56)(57,103,66,97,71,76,58,104,65,98,72,75)(59,95,73,86,82,92,60,96,74,85,81,91)(61,90,80,87,69,93,62,89,79,88,70,94)(63,100,67,101,83,78,64,99,68,102,84,77);(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, 240797);