Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C24×Dic15 |
| derived, Hall | C3×C5 ⋊ C24×C4 |
| Sylow | C5 ⋊ C24×Dic3 |
| Sylow | C3 ⋊ C24×Dic5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | D15 |
| commutator, hypocenter | C3×C5 | C24×C4 |
| Frattini | C2 | C24×D15 |
| Fitting, socle, prime radical | C25×C3×C5 | C2 |
| cosocle | C2×C3×C5 | C25 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C25 | |
2724 conjugacy classes of subgroups.
| transitive degree | μt(G) = 960 |
288 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #14279861, #14279876, C22×#91115, … |
| maximal normal subgroup of | #14279861, #14279876, C22×#91115, … |
| maximal quotient of | C23×C4×Dic15, C23×#6719, C23×C4⋊Dic15, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 11346);