Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C32 · Schur multiplier (H2) = C2 |
| direct product | C2×C5×C3⋊C32 |
| unambiguous semidirect product | (C2×C3)⋊(C5×C32) |
| derived, Sylow | C3 ⋊ C2×C5×C32 |
| Hall | C3×C5 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5×C16 | D3 |
| commutator, hypocenter | C3 | C2×C5×C32 |
| Frattini | C16 | C2×C5×D3 |
| Fitting | C2×C3×C5×C16 | C2 |
| socle, prime radical | C22×C3×C5 | C16 |
| cosocle | C3×C16 | C22×C5 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C2×C5×C16 | |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 960 |
480 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×Dic3×C32, C4×C5×C3⋊C32, Dic5×C3⋊C32, … |
| maximal normal subgroup of | C5×Dic3×C32, C4×C5×C3⋊C32, Dic5×C3⋊C32, … |
| maximal quotient of | C4×C5×C3⋊C32, C5×#67803, C5×C4⋊(C3⋊C32), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 392);