Finite Group DatabasebetaFinite Group Databasebeta| order | 8228 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11 · Schur multiplier (H2) = C2 |
| direct product | C11×D11×D17 |
| unambiguous semidirect product | (C17×D11)⋊(C2×C11) |
| unambiguous semidirect product | (C11×D17)⋊(C2×C11) |
| unambiguous semidirect product | D187⋊(C2×C11) |
| Fitting, socle, Hall | C112×C17 ⋊ C22 |
| derived | C11×C17 ⋊ C22×C11 |
| Sylow | C112 ⋊ C2×D17 |
| Sylow | C17 ⋊ C2×C11×D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D11×D17 |
| commutator, hypocenter | C11×C17 | C22×C11 |
| Frattini | C1 | G |
| Fitting, socle | C112×C17 | C22 |
| LCS | G ▷ C11×C17 | |
| UCS | C1 ◁ C11 | |
60 conjugacy classes of subgroups.
770 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#10624391, C3×C11×D11×D17, C11×D17×D33, … |
| maximal normal subgroup of | C3×C11×D11×D17 |
| maximal quotient of | C3×C11×D11×D17, C11×D17×D33, C11×D11×D51, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8228, 21);