Finite Group DatabasebetaFinite Group Databasebeta| order | 8226 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C2×C3×C457⋊C3 |
| unambiguous semidirect product | (C2×C457)⋊C32 |
| unambiguous semidirect product | (C2×C3×C457)⋊C3 |
| Fitting, socle | C2×C3×C457 ⋊ C3 |
| derived, Sylow | C457 ⋊ C2×C32 |
| Hall | C2×C457 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C457⋊C3 |
| commutator, hypocenter | C457 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C457 | C3 |
| LCS | G ▷ C457 | |
| UCS | C1 ◁ C2×C3 | |
24 conjugacy classes of subgroups.
930 conjugacy classes — view the full character table.
| maximal subgroup of | C3×Dic457⋊C3, C3⋊(Dic457⋊C3), Dic3×C457⋊C3, … |
| maximal normal subgroup of | C3×Dic457⋊C3, C3⋊(Dic457⋊C3), Dic3×C457⋊C3, … |
| maximal quotient of | C3×C4×C457⋊C3, C22×C3×C457⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8226, 11);