Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | C2×#91572 |
| Hall | C3×C5 ⋊ C2×#120 |
| Sylow | C5 ⋊ C2×#937 |
| Sylow | C3 ⋊ C2×#4028 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×D3×D5 |
| commutator, cosocle | C22×C3×C5 | C24 |
| Frattini | C22 | C22×D3×D5 |
| Fitting | C24×C3×C5 | C22 |
| socle | C23×C3×C5 | C23 |
| hypercenter | C24 | D3×D5 |
| hypocenter | C3×C5 | C2×#120 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C23 ◁ C24 | |
1324 conjugacy classes of subgroups; only the 208 normal subgroups are shown.
This group has 1324 conjugacy classes of subgroups — too many to draw. Only its 208 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | #14301631, #14301637, #14302055, … |
| maximal normal subgroup of | #14301631, #14301637, #14302055, … |
| maximal quotient of | C2×#11749502, C2×#11748729, C2×#11749517, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 9619);