Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | D3×#4076 |
| Fitting | C22×C3×C4×C5 ⋊ C22 |
| Hall | C3×C5 ⋊ C2×#121 |
| Sylow | C5 ⋊ D3×#121 |
| Sylow | C3 ⋊ C2×#4076 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D3×D5 |
| commutator, socle, cosocle | C22×C3×C5 | C24 |
| Fitting | C22×C3×C4×C5 | C22 |
| hypercenter | C22×C4 | D3×D5 |
| hypocenter | C3×C5 | C2×#121 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ C22×C4 | |
852 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
138 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#64671, D3×#64690, #14283127, … |
| maximal normal subgroup of | D3×#64671, D3×#64690, #14283127, … |
| maximal quotient of | D3×#65501, D3×#65502, D3×#65229, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 8849);