Finite Group DatabasebetaFinite Group Databasebeta| order | 8772 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D43×D51 |
| unambiguous semidirect product | (C3×D43)⋊D17 |
| unambiguous semidirect product | (C17×D43)⋊D3 |
| Fitting, socle, derived, Hall | C3×C17×C43 ⋊ C22 |
| Hall | C17×C43 ⋊ C2×D3 |
| Hall | C3×C43 ⋊ C2×D17 |
| Hall | C3×C17 ⋊ C2×D43 |
| Sylow | C43 ⋊ C2×D51 |
| Sylow | C17 ⋊ D3×D43 |
| Sylow | C3 ⋊ D17×D43 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C17×C43 | C22 |
| LCS | G ▷ C3×C17×C43 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
621 conjugacy classes — view the full character table.
| maximal subgroup of | D43×D153, D51×D43⋊C3, C3×D43×D51, … |
| maximal normal subgroup of | D51×D43⋊C3, C3×D43×D51 |
| maximal quotient of | D43×D153, C3×D43×D51, D129⋊D51, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8772, 26);