Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (A5⋊C4)⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×S5 |
| commutator | C2×A5 | C2×C4 |
| Fitting, hypercenter | C2×C4 | S5 |
| socle, prime radical, cosocle | C22×A5 | C22 |
| hypocenter | A5 | C4⋊C4 |
| LCS | G ▷ C2×A5 ▷ A5 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
193 conjugacy classes of subgroups; only the 17 normal subgroups are shown.
This group has 193 conjugacy classes of subgroups — too many to draw. Only its 17 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
Permutation generators:
(1,2,3,4)(7,8)(9,13)(10,12);(5,8,6,7)(9,13,10)(11,12)38 conjugacy classes — view the full character table.
| maximal subgroup of | C2×(A5⋊C4)⋊C4, C4⋊C4×S5, #14514793, … |
| maximal normal subgroup of | C2×(A5⋊C4)⋊C4, C4⋊C4×S5, #14514793, … |
| maximal quotient of | A5⋊#95, (A5⋊C4)⋊C8, #14514757, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5703);