Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
| direct product | S4×D20 |
| Fitting | C22×C4×C5 ⋊ C2×D3 |
| Sylow | C5 ⋊ D4×S4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D5×S4 |
| commutator, cosocle | C2×C5×A4 | C23 |
| Fitting | C22×C4×C5 | C2×D3 |
| socle | C23×C5 | C22×D3 |
| hypercenter | C4 | D5×S4 |
| hypocenter | C5×A4 | C2×D4 |
| LCS | G ▷ C2×C5×A4 ▷ C5×A4 | |
| UCS | C1 ◁ C2 ◁ C4 | |
468 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 60 |
65 conjugacy classes — view the full character table.
| maximal subgroup of | S4×#677, #14512921, S4×D40, … |
| maximal normal subgroup of | S4×#677, #14512921, S4×D40, … |
| maximal quotient of | #14512704, #14512750, #14512751, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10952);