Finite Group DatabasebetaFinite Group Databasebeta| order | 8772 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C17 · Schur multiplier (H2) = C2 |
| direct product | D3×C17×D43 |
| unambiguous semidirect product | (D3×C43)⋊(C2×C17) |
| unambiguous semidirect product | (C3×D43)⋊(C2×C17) |
| unambiguous semidirect product | D129⋊(C2×C17) |
| Fitting, socle, Hall | C3×C17×C43 ⋊ C22 |
| derived, Hall | C3×C43 ⋊ C22×C17 |
| Hall | C17×C43 ⋊ C2×D3 |
| Hall | C3×C17 ⋊ C2×D43 |
| Sylow | C43 ⋊ C2×D3×C17 |
| Sylow | C3 ⋊ C2×C17×D43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | D3×D43 |
| commutator, hypocenter | C3×C43 | C22×C17 |
| Frattini | C1 | G |
| Fitting, socle | C3×C17×C43 | C22 |
| LCS | G ▷ C3×C43 | |
| UCS | C1 ◁ C17 | |
40 conjugacy classes of subgroups.
1173 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C17×D9×D43, D3×C17×D43⋊C3, C3×D3×C17×D43, … |
| maximal normal subgroup of | D3×C17×D43⋊C3, C3×D3×C17×D43 |
| maximal quotient of | C17×D9×D43, C3×D3×C17×D43, D3×C17×D129, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8772, 23);