Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of C5⋊S4 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2×C4 |
| direct product | C4×A4⋊Dic5 |
| derived | C5×A4 ⋊ C42 |
| Sylow | C5 ⋊ C4×SL(2,ℤ/4) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | C5⋊S4 |
| commutator, hypocenter | C5×A4 | C42 |
| Frattini | C22 | C2×C5⋊S4 |
| Fitting | C23×C4×C5 | D3 |
| socle | C24×C5 | C2×D3 |
| prime radical, cosocle | C22×C5×A4 | C22 |
| LCS | G ▷ C5×A4 | |
| UCS | C1 ◁ C2×C4 | |
250 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
104 conjugacy classes — view the full character table.
| maximal subgroup of | #14511766, #14511767, #14511770, … |
| maximal normal subgroup of | #14511766, #14511767, #14511770, … |
| maximal quotient of | C4×A4⋊#168, #14511958, C4×#91184, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6324);