Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×#6780 |
| Hall | C3×C5 ⋊ C22×#41 |
| Sylow | C5 ⋊ C22×#237 |
| Sylow | C3 ⋊ C22×#711 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×D3×D5 |
| commutator, cosocle | C2×C3×C5 | C25 |
| Frattini | C2 | C23×D3×D5 |
| Fitting | C24×C3×C5 | C22 |
| socle | C23×C3×C5 | C23 |
| hypercenter | C24 | D3×D5 |
| hypocenter | C3×C5 | C22×#41 |
| LCS | G ▷ C2×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C23 ◁ C24 | |
1780 conjugacy classes of subgroups; only the 568 normal subgroups are shown.
This group has 1780 conjugacy classes of subgroups — too many to draw. Only its 568 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 480 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | #14296872, #14296881, #14296971, … |
| maximal normal subgroup of | #14296872, #14296881, #14296971, … |
| maximal quotient of | C22×#91400, C22×#91394, C22×#91532, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 11262);