Finite Group DatabasebetaFinite Group Databasebeta| order | 1656 |
| isoclinism | isoclinic class of D69 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C22×C3×D69 |
| Fitting, socle | C22×C32×C23 ⋊ C2 |
| derived | C3×C23 ⋊ C23×C3 |
| Hall | C32×C23 ⋊ C23 |
| Sylow | C23 ⋊ C22×C3×D3 |
| Sylow | C32 ⋊ C22×D23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | D69 |
| commutator, cosocle, hypocenter | C3×C23 | C23×C3 |
| Frattini | C1 | G |
| Fitting, socle | C22×C32×C23 | C2 |
| LCS | G ▷ C3×C23 | |
| UCS | C1 ◁ C22×C3 | |
138 conjugacy classes of subgroups.
| transitive degree | μt(G) = 552 |
432 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1656, 134);