Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C43×C5 · Schur multiplier (H2) = C43 |
| direct product | C42×C5×Dic3 |
| unambiguous semidirect product | C3⋊(C43×C5) |
| derived, Sylow | C3 ⋊ C43×C5 |
| Hall | C3×C5 ⋊ C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C42×C5 | D3 |
| commutator, hypocenter | C3 | C43×C5 |
| Frattini | C23 | C22×C5×D3 |
| Fitting | C2×C3×C42×C5 | C2 |
| socle, prime radical | C23×C3×C5 | C23 |
| cosocle | C23×C3 | C23×C5 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C2×C42×C5 | |
516 conjugacy classes of subgroups.
| transitive degree | μt(G) = 960 |
480 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×#67736, #14276740, C4×C5×C8×Dic3, … |
| maximal normal subgroup of | C5×#67736, #14276740, C4×C5×C8×Dic3, … |
| maximal quotient of | C5×Dic3×#95, C4×C5×C3⋊#95, C4×C5×C8×Dic3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4624);