Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#6729 |
| 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 | |
145 conjugacy classes of subgroups; only the 14 normal subgroups are shown.
This group has 145 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) = 160 |
Permutation generators:
(1,3,2,4)(5,17,32,15,10)(6,18,31,16,9)(7,20,34,25,14)(8,19,33,26,13)(11,36,42,37,22)(12,35,41,38,21)(23,30,28,43,39)(24,29,27,44,40);(1,3)(2,4)(5,7,26,17,6,8,25,18)(9,11,42,31,10,12,41,32)(13,40,35,43,14,39,36,44)(15,19,29,33,16,20,30,34)(21,38,27,24,22,37,28,23)33 conjugacy classes — view the full character table.
| maximal subgroup of | #14515006, #14515007, #14515010, … |
| maximal normal subgroup of | #14515006, #14515007, #14515010, … |
| maximal quotient of | #14514939, C4⋊#91143, #14515010, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5699);