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, socle | C2 | D4×S5 |
| commutator, cosocle | #6732 | C23 |
| Frattini | C4 | C22×S5 |
| Fitting, hypercenter | Q16 | S5 |
| hypocenter | SL(2,𝔽5) | C2×D4 |
| LCS | G ▷ #6732 ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C2 ◁ C4 ◁ Q16 | |
428 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 26 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 96 |
| transitive degree | μt(G) = 96 |
Permutation generators:
(1,20,28,26,14,37,8,41,18,44,39,11,2,19,27,25,13,38,7,42,17,43,40,12)(3,29,9,23,45,36,22,47,31,5,33,15,4,30,10,24,46,35,21,48,32,6,34,16)(49,68,79,91,88,84,55,90,57,73,61,64,50,67,80,92,87,83,56,89,58,74,62,63)(51,78,66,54,81,85,69,95,76,72,93,60,52,77,65,53,82,86,70,96,75,71,94,59);(1,47,28,41,22,35)(2,48,27,42,21,36)(3,15,7,29,17,20)(4,16,8,30,18,19)(5,31,26,34,37,40)(6,32,25,33,38,39)(9,43,46,12,13,23)(10,44,45,11,14,24)(49,84,70,90,76,96)(50,83,69,89,75,95)(51,67,65,78,55,64)(52,68,66,77,56,63)(53,87,85,81,74,80)(54,88,86,82,73,79)(57,72,61,59,94,92)(58,71,62,60,93,91);(1,49)(2,50)(3,51)(4,52)(5,53)(6,54)(7,55)(8,56)(9,57)(10,58)(11,59)(12,60)(13,61)(14,62)(15,63)(16,64)(17,65)(18,66)(19,67)(20,68)(21,69)(22,70)(23,71)(24,72)(25,73)(26,74)(27,75)(28,76)(29,77)(30,78)(31,79)(32,80)(33,81)(34,82)(35,83)(36,84)(37,85)(38,86)(39,87)(40,88)(41,89)(42,90)(43,91)(44,92)(45,93)(46,94)(47,95)(48,96)39 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240857);