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 | C4 | C22⋊S5 |
| commutator, cosocle | #6732 | C23 |
| Frattini | C4 | C22×S5 |
| Fitting, hypercenter | #41 | S5 |
| socle | C2 | C2×C22⋊S5 |
| hypocenter | SL(2,𝔽5) | C2×D4 |
| LCS | G ▷ #6732 ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C4 ◁ C2×C4 ◁ #41 | |
509 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 509 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.
| minimal degree | μ(G) = 48 |
| transitive degree | μt(G) = 48 |
Permutation generators:
(3,12,17,6,19,25,7,22,23,14,9,15,4,11,18,5,20,26,8,21,24,13,10,16)(29,49,51,31,48,46,34,43,42,40,38,35,30,50,52,32,47,45,33,44,41,39,37,36);(1,2)(3,15,22,5,24,8,25,12,14,18,4,16,21,6,23,7,26,11,13,17)(9,19,10,20)(27,28)(29,36,40,51,37,34,46,32,42,48,30,35,39,52,38,33,45,31,41,47)(43,50,44,49);(1,27)(2,28)(3,29)(4,30)(5,31)(6,32)(7,33)(8,34)(9,35)(10,36)(11,37)(12,38)(13,39)(14,40)(15,41)(16,42)(17,43)(18,44)(19,45)(20,46)(21,47)(22,48)(23,49)(24,50)(25,51)(26,52)48 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240813);