Finite Group DatabasebetaFinite Group Databasebeta| order | 8228 |
| isoclinism | isoclinic class of D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11×C17 · Schur multiplier (H2) = C2 |
| direct product | C2×C11×C17×D11 |
| unambiguous semidirect product | C11⋊(C22×C11×C17) |
| unambiguous semidirect product | (C2×C11)⋊(C2×C11×C17) |
| Fitting, socle | C2×C112×C17 ⋊ C2 |
| derived | C11 ⋊ C22×C11×C17 |
| Hall | C112×C17 ⋊ C22 |
| Sylow | C112 ⋊ C22×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11×C17 | D11 |
| commutator, hypocenter | C11 | C22×C11×C17 |
| Frattini | C1 | G |
| Fitting, socle | C2×C112×C17 | C2 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C2×C11×C17 | |
60 conjugacy classes of subgroups.
2618 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C17×#10624391, D3×C11×C17×D11, C2×C3×C11×C17×D11, … |
| maximal normal subgroup of | C2×C3×C11×C17×D11 |
| maximal quotient of | D3×C11×C17×D11, C2×C3×C11×C17×D11, C2×C11×C17×D33 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8228, 33);