Finite Group DatabasebetaFinite Group Databasebeta| order | 1656 |
| isoclinism | isoclinic class of #157×D23 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | #157×D23 |
| Fitting, socle, derived, Hall | C32×C23 ⋊ C2×C4 |
| Sylow | C23 ⋊ C2×#157 |
| Sylow | C32 ⋊ C4×D23 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C23 | C2×C4 |
| prime radical | C3⋊D3×D23 | C2 |
| cosocle | C3⋊D3×C23 | C22 |
| LCS | G ▷ C32×C23 | |
| UCS | C1 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 138 |
78 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1656, 110);