Finite Group DatabasebetaFinite Group Databasebeta| order | 8676 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×Dic241⋊C3 |
| unambiguous semidirect product | Dic241⋊C32 |
| unambiguous semidirect product | (C3×Dic241)⋊C3 |
| derived, Sylow | C241 ⋊ C32×C4 |
| Hall | C3×C241⋊C3 ⋊ C4 |
| Hall | Dic241 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D241⋊C3 |
| commutator, hypocenter | C241 | C32×C4 |
| Frattini | C2 | C3×D241⋊C3 |
| Fitting, socle | C2×C3×C241 | C2×C3 |
| LCS | G ▷ C241 | |
| UCS | C1 ◁ C2×C3 | |
36 conjugacy classes of subgroups.
276 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8676, 20);