Finite Group DatabasebetaFinite Group Databasebeta| order | 1656 |
| isoclinism | isoclinic class of D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C23 · Schur multiplier (H2) = C23 |
| direct product | C2×D32×C23 |
| unambiguous semidirect product | (C3×D3)⋊(C22×C23) |
| unambiguous semidirect product | (C3⋊D3)⋊(C22×C23) |
| Fitting, socle | C2×C32×C23 ⋊ C22 |
| derived, Sylow | C32 ⋊ C23×C23 |
| Hall | C32×C23 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C23 | D32 |
| commutator, cosocle, hypocenter | C32 | C23×C23 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C23 | C22 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C2×C23 | |
138 conjugacy classes of subgroups.
| transitive degree | μt(G) = 276 |
414 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1656, 128);