Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| direct product | D15×C32 |
| Fitting | C3×C5×C32 ⋊ C2 |
| derived, Hall | C3×C5 ⋊ C2×C32 |
| Sylow | C5 ⋊ D3×C32 |
| Sylow | C3 ⋊ D5×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | D15 |
| commutator, hypocenter | C3×C5 | C2×C32 |
| Frattini | C16 | C2×D15 |
| Fitting | C3×C5×C32 | C2 |
| socle | C2×C3×C5 | C2×C16 |
| prime radical | C2×D15 | C16 |
| cosocle | C3×C5×C16 | C22 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C32 | |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 480 |
288 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D15×C64, #14279786, #14279792, … |
| maximal normal subgroup of | D15×C64, #14279786, #14279792, … |
| maximal quotient of | C32×Dic15, #14279243, #14279685, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 462);