Finite Group DatabasebetaFinite Group Databasebeta| order | 8772 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | #595×C43⋊C3 |
| unambiguous semidirect product | (C43×#595)⋊C3 |
| Fitting, socle, derived, Hall | C17×C43 ⋊ C3×C4 |
| Hall | C43×#595 ⋊ C3 |
| Hall | C17×C43⋊C3 ⋊ C4 |
| Sylow | C43 ⋊ C3×#595 |
| Sylow | C17 ⋊ C4×C43⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C17×C43 | C3×C4 |
| LCS | G ▷ C17×C43 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
136 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#595×C43⋊C3, C43⋊C3×C3⋊#595 |
| maximal normal subgroup of | C3×#595×C43⋊C3 |
| maximal quotient of | #595×C43⋊C9, C3×#595×C43⋊C3, C43⋊C3×C3⋊#595 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8772, 15);