Finite Group DatabasebetaFinite Group Databasebeta| order | 8772 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C43⋊C3)⋊Dic17 |
| unambiguous semidirect product | Dic731⋊C3 |
| derived, Hall | C17×C43 ⋊ C3×C4 |
| Hall | Dic731 ⋊ C3 |
| Hall | C17×C43⋊C3 ⋊ C4 |
| Hall | C43⋊C3 ⋊ Dic17 |
| Sylow | C43 ⋊ C3×Dic17 |
| Sylow | C17 ⋊ (C43⋊C3)⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C17⋊(D43⋊C3) |
| commutator, hypocenter | C17×C43 | C3×C4 |
| Fitting, socle | C2×C17×C43 | C2×C3 |
| LCS | G ▷ C17×C43 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,17,43,2|a^2=e,c^a=c^16,d^a=d^42,d^b=d^36298 conjugacy classes — view the full character table.
| maximal subgroup of | C3×(C43⋊C3)⋊Dic17, C3⋊((C43⋊C3)⋊Dic17) |
| maximal normal subgroup of | C3×(C43⋊C3)⋊Dic17 |
| maximal quotient of | (C43⋊C9)⋊Dic17, C3×(C43⋊C3)⋊Dic17, C3⋊((C43⋊C3)⋊Dic17) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8772, 12);