Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊#6729 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle | C22 | C2×S5 |
| commutator, cosocle | C2×SL(2,𝔽5) | C22 |
| Fitting, hypercenter | C23 | S5 |
| hypocenter | SL(2,𝔽5) | D4 |
| LCS | G ▷ C2×SL(2,𝔽5) ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C22 ◁ C23 | |
148 conjugacy classes of subgroups; only the 14 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 14 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)(5,27,22,6,28,21)(7,17,38,8,18,37)(9,36,44,10,35,43)(11,29,39,12,30,40)(13,33,32,14,34,31)(15,20,41,16,19,42)(23,24)(25,26);(3,4)(5,39,36,25,6,40,35,26)(7,9,27,41,8,10,28,42)(11,20,17,30,12,19,18,29)(13,32,44,22,14,31,43,21)(15,24,37,34,16,23,38,33)33 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C22⋊#6729, #14515097, #14515098, … |
| maximal normal subgroup of | C2×C22⋊#6729, #14515097, #14515098, … |
| maximal quotient of | C22⋊#91143, #14514939, #14514968, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5723);