Finite Group DatabasebetaFinite Group Databasebeta| order | 8228 |
| isoclinism | isoclinic class of D187 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11 · Schur multiplier (H2) = C2 |
| direct product | C2×C11×D187 |
| unambiguous semidirect product | (C2×C11)⋊(C11×D17) |
| unambiguous semidirect product | (C2×C17)⋊(C11×D11) |
| Fitting, socle | C2×C112×C17 ⋊ C2 |
| derived | C11×C17 ⋊ C22×C11 |
| Hall | C112×C17 ⋊ C22 |
| Sylow | C112 ⋊ C2×D17 |
| Sylow | C17 ⋊ C2×C11×D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11 | D187 |
| commutator, hypocenter | C11×C17 | C22×C11 |
| Frattini | C1 | G |
| Fitting, socle | C2×C112×C17 | C2 |
| LCS | G ▷ C11×C17 | |
| UCS | C1 ◁ C2×C11 | |
60 conjugacy classes of subgroups.
2090 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C17⋊#10624391, D3×C11×D187, C2×C3×C11×D187, … |
| maximal normal subgroup of | C2×C3×C11×D187 |
| maximal quotient of | D3×C11×D187, C2×C3×C11×D187, C2×C11×D561 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8228, 32);