Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | D4×#1203 |
| Hall | C3×C5 ⋊ D42 |
| Sylow | C5 ⋊ D4×D12 |
| Sylow | C3 ⋊ D4×C22⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D3×D5 |
| commutator, socle, cosocle | C22×C3×C5 | C24 |
| Fitting | C2×C3×C5×D4 | C22 |
| hypercenter | C2×D4 | D3×D5 |
| hypocenter | C3×C5 | D42 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
856 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
105 conjugacy classes — view the full character table.
| maximal subgroup of | #14453284, #14453286, #14453296, … |
| maximal normal subgroup of | #14453284, #14453286, #14453296, … |
| maximal quotient of | C22⋊C4×#1203, D4×#6667, D4×(C2×D3)⋊Dic5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 9122);