Finite Group DatabasebetaFinite Group Databasebeta| order | 8772 |
| isoclinism | isoclinic class of D43⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C17 · Schur multiplier (H2) = C2 |
| Fitting, socle | C2×C17×C43 ⋊ C2×C3 |
| derived, Sylow | C43 ⋊ C22×C3×C17 |
| Hall | C2×C17×D43 ⋊ C3 |
| Hall | C17×C43⋊C3 ⋊ C22 |
| Hall | C17×C43 ⋊ C22×C3 |
| Hall | C2×D43 ⋊ C3×C17 |
| Hall | C43⋊C3 ⋊ C22×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C17 | D43⋊C3 |
| commutator, hypocenter | C43 | C22×C3×C17 |
| Frattini | C1 | G |
| Fitting, socle | C2×C17×C43 | C2×C3 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C2×C17 | |
40 conjugacy classes of subgroups.
442 conjugacy classes — view the full character table.
| maximal subgroup of | D3×C17×D43⋊C3, C2×C3×C17×D43⋊C3, C2×C17×C3⋊(D43⋊C3) |
| maximal normal subgroup of | C2×C3×C17×D43⋊C3 |
| maximal quotient of | C2×C17×D43⋊C9, D3×C17×D43⋊C3, C2×C3×C17×D43⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8772, 17);