Finite Group DatabasebetaFinite Group Databasebeta| order | 11649 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C11 · Schur multiplier (H2) = C1 |
| direct product | C3×C353⋊C11 |
| unambiguous semidirect product | C353⋊(C3×C11) |
| unambiguous semidirect product | (C3×C353)⋊C11 |
| Fitting, socle, Hall | C3×C353 ⋊ C11 |
| derived, Sylow | C353 ⋊ C3×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C353⋊C11 |
| commutator, cosocle, hypocenter | C353 | C3×C11 |
| Frattini | C1 | G |
| Fitting, socle | C3×C353 | C11 |
| LCS | G ▷ C353 | |
| UCS | C1 ◁ C3 | |
8 conjugacy classes of subgroups.
129 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3×C353⋊C11, C3×D353⋊C11, D3×C353⋊C11, … |
| maximal normal subgroup of | C2×C3×C353⋊C11, C3×D353⋊C11, D3×C353⋊C11, … |
| maximal quotient of | C2×C3×C353⋊C11, C9×C353⋊C11, C32×C353⋊C11 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11649, 1);