Finite Group DatabasebetaFinite Group Databasebeta| order | 8226 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C32×D457 |
| Fitting, socle, Hall | C32×C457 ⋊ C2 |
| derived, Sylow | C457 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | D457 |
| commutator, hypocenter | C457 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C32×C457 | C2 |
| LCS | G ▷ C457 | |
| UCS | C1 ◁ C32 | |
24 conjugacy classes of subgroups.
2070 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×#14270052, C3×C3⋊#14270052, C3×D3×D457, … |
| maximal normal subgroup of | C32×#14270052, C3×C3⋊#14270052, C3×D3×D457, … |
| maximal quotient of | C32×Dic457, C2×C32×D457 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8226, 12);