Finite Group DatabasebetaFinite Group Databasebeta| order | 9228 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D3×D769 |
| unambiguous semidirect product | (D3×C769)⋊C2 |
| unambiguous semidirect product | (C3×D769)⋊C2 |
| unambiguous semidirect product | D2307⋊C2 |
| Fitting, socle, derived, Hall | C3×C769 ⋊ C22 |
| Sylow | C769 ⋊ C2×D3 |
| Sylow | C3 ⋊ C2×D769 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C769 | C22 |
| LCS | G ▷ C3×C769 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
1158 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D9×D769, D3×D769⋊C3, C3×D3×D769, … |
| maximal normal subgroup of | D3×D769⋊C3, C3×D3×D769 |
| maximal quotient of | D9×D769, C3×D3×D769, D3×D2307, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9228, 12);