Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle | C22 | C2×S5 |
| commutator, cosocle | C2×SL(2,𝔽5) | C22 |
| Fitting, hypercenter | C2×C4 | S5 |
| hypocenter | SL(2,𝔽5) | D4 |
| LCS | G ▷ C2×SL(2,𝔽5) ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
146 conjugacy classes of subgroups; only the 12 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 12 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:
(1,4)(2,3)(5,29,11,15,6,30,12,16)(7,44,23,10,8,43,24,9)(13,28,38,20,14,27,37,19)(17,40,35,21,18,39,36,22)(25,41,32,33,26,42,31,34);(1,3,2,4)(5,42,35,14,40,34)(6,41,36,13,39,33)(7,16,22,8,15,21)(9,17,29)(10,18,30)(11,28,24,25,44,20)(12,27,23,26,43,19)(31,37)(32,38)33 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11751514, #14515097, #14515099, … |
| maximal normal subgroup of | C2×#11751514, #14515097, #14515099, … |
| maximal quotient of | #14514929, #14514939, #14514967, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5709);