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 | C2×D4 | S5 |
| hypocenter | SL(2,𝔽5) | C2×D4 |
| LCS | G ▷ C2×SL(2,𝔽5) ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
462 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 462 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) = 192 |
Permutation generators:
(5,40,13,30,34,51,6,39,14,29,33,52)(7,37,15,32,36,50,8,38,16,31,35,49)(9,47,23,18,27,41,10,48,24,17,28,42)(11,46,22,20,26,43,12,45,21,19,25,44)(57,92,65,82,86,103,58,91,66,81,85,104)(59,89,67,84,88,102,60,90,68,83,87,101)(61,99,75,70,79,93,62,100,76,69,80,94)(63,98,74,72,78,95,64,97,73,71,77,96);(1,3,2,4)(5,31,36,44,28,51,6,32,35,43,27,52)(7,30,33,41,25,50,8,29,34,42,26,49)(9,47,16,40,22,19,10,48,15,39,21,20)(11,46,13,37,24,18,12,45,14,38,23,17)(53,56,54,55)(57,84,88,95,80,104,58,83,87,96,79,103)(59,81,85,94,77,101,60,82,86,93,78,102)(61,100,68,91,74,72,62,99,67,92,73,71)(63,97,65,90,76,69,64,98,66,89,75,70);(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, 240841);