Finite Group DatabasebetaFinite Group Databasebeta| order | 9231 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×C181⋊C3 |
| unambiguous semidirect product | C181⋊(C3×C17) |
| unambiguous semidirect product | (C17×C181)⋊C3 |
| Fitting, socle, Hall | C17×C181 ⋊ C3 |
| derived, Sylow | C181 ⋊ C3×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | C181⋊C3 |
| commutator, hypocenter | C181 | C3×C17 |
| Frattini | C1 | G |
| Fitting, socle | C17×C181 | C3 |
| LCS | G ▷ C181 | |
| UCS | C1 ◁ C17 | |
8 conjugacy classes of subgroups.
1071 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C17×C181⋊C3, C17×D181⋊C3, D17×C181⋊C3, … |
| maximal normal subgroup of | C2×C17×C181⋊C3, C17×D181⋊C3, D17×C181⋊C3, … |
| maximal quotient of | C2×C17×C181⋊C3, C17×#13108656, C3×C17×C181⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9231, 1);