Finite Group DatabasebetaFinite Group Databasebeta| order | 8228 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C11 |
| direct product | D17×C11⋊D11 |
| unambiguous semidirect product | (C11×D17)⋊D11 |
| Fitting, socle, derived, Hall | C112×C17 ⋊ C22 |
| Sylow | C112 ⋊ C2×D17 |
| Sylow | C17 ⋊ C2×C11⋊D11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C112×C17 | C22 |
| LCS | G ▷ C112×C17 | |
| UCS | C1 | |
140 conjugacy classes of subgroups.
620 conjugacy classes — view the full character table.
| maximal subgroup of | D17×(C11⋊D11)⋊C3, C3×D17×C11⋊D11, D17×C3⋊(C11⋊D11), … |
| maximal normal subgroup of | D17×(C11⋊D11)⋊C3, C3×D17×C11⋊D11 |
| maximal quotient of | C3×D17×C11⋊D11, D17×C3⋊(C11⋊D11), D51×C11⋊D11, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8228, 23);