Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C5 · Schur multiplier (H2) = C215 |
| direct product | C25×C5×D3 |
| unambiguous semidirect product | C3⋊(C26×C5) |
| unambiguous semidirect product | (C2×C3)⋊(C25×C5) |
| Fitting, socle | C25×C3×C5 ⋊ C2 |
| derived, Sylow | C3 ⋊ C26×C5 |
| Hall | C3×C5 ⋊ C26 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25×C5 | D3 |
| commutator, cosocle, hypocenter | C3 | C26×C5 |
| Frattini | C1 | G |
| Fitting, socle | C25×C3×C5 | C2 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C25×C5 | |
11300 conjugacy classes of subgroups.
| transitive degree | μt(G) = 480 |
480 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 11392);