Finite Group DatabasebetaFinite Group Databasebeta| order | 11898 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C3×D661⋊C3 |
| unambiguous semidirect product | D661⋊C32 |
| unambiguous semidirect product | (C661⋊C3)⋊(C2×C3) |
| unambiguous semidirect product | (C3×D661)⋊C3 |
| Fitting, socle | C3×C661 ⋊ C2×C3 |
| derived, Sylow | C661 ⋊ C2×C32 |
| Hall | C3×C661⋊C3 ⋊ C2 |
| Hall | D661 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D661⋊C3 |
| commutator, cosocle, hypocenter | C661 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C661 | C2×C3 |
| LCS | G ▷ C661 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
348 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#14581558⋊C3, C3⋊(#14581558⋊C3), D3×D661⋊C3, … |
| maximal normal subgroup of | C3×#14581558⋊C3, C3⋊(#14581558⋊C3), D3×D661⋊C3, … |
| maximal quotient of | C3×Dic661⋊C3, C2×C3×D661⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11898, 8);