Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of C5⋊S4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | C23×C5⋊S4 |
| Fitting, socle | C25×C5 ⋊ D3 |
| derived | C5×A4 ⋊ C24 |
| Sylow | C5 ⋊ C23×S4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | C5⋊S4 |
| commutator, cosocle, hypocenter | C5×A4 | C24 |
| Frattini | C1 | G |
| Fitting, socle | C25×C5 | D3 |
| LCS | G ▷ C5×A4 | |
| UCS | C1 ◁ C23 | |
1402 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 1402 conjugacy classes of subgroups — too many to draw. Only its 147 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
104 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11751638, #14513653, #14513659, … |
| maximal normal subgroup of | C2×#11751638, #14513653, #14513659, … |
| maximal quotient of | C22×#91948, C22×C4×C5⋊S4, C22×C4⋊(C5⋊S4), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 11379);