Finite Group DatabasebetaFinite Group Databasebeta| order | 1656 |
| isoclinism | isoclinic class of D69 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×Dic69 |
| unambiguous semidirect product | (C2×C3)⋊(C3×Dic23) |
| unambiguous semidirect product | (C2×C23)⋊(C3×Dic3) |
| derived | C3×C23 ⋊ C2×C3×C4 |
| Hall | C32×C23 ⋊ C2×C4 |
| Sylow | C23 ⋊ C2×C3×Dic3 |
| Sylow | C32 ⋊ C2×Dic23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | D69 |
| commutator, hypocenter | C3×C23 | C2×C3×C4 |
| Frattini | C2 | C2×C3×D69 |
| Fitting, socle, prime radical | C22×C32×C23 | C2 |
| cosocle | C2×C3×C23 | C22×C3 |
| LCS | G ▷ C3×C23 | |
| UCS | C1 ◁ C22×C3 | |
74 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, 93);