Finite Group DatabasebetaFinite Group Databasebeta| order | 11268 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×D313⋊C9 |
| unambiguous semidirect product | D313⋊(C2×C9) |
| unambiguous semidirect product | (C2×D313)⋊C9 |
| unambiguous semidirect product | (C313⋊C9)⋊C22 |
| unambiguous semidirect product | (C2×C313⋊C9)⋊C2 |
| derived, Sylow | C313 ⋊ C22×C9 |
| Hall | C313⋊C9 ⋊ C22 |
| Hall | C2×D313 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D313⋊C3 |
| commutator, hypocenter | C313 | C22×C9 |
| Frattini | C3 | C2×D313⋊C3 |
| Fitting, socle | C2×C3×C313 | C2×C3 |
| prime radical | C2×C3×D313 | C3 |
| cosocle | C3×C313 | C22×C3 |
| LCS | G ▷ C313 | |
| UCS | C1 ◁ C2×C3 | |
30 conjugacy classes of subgroups.
348 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11268, 9);