Finite Group DatabasebetaFinite Group Databasebeta| order | 11892 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×D991⋊C3 |
| unambiguous semidirect product | D991⋊(C2×C3) |
| unambiguous semidirect product | (C991⋊C3)⋊C22 |
| unambiguous semidirect product | (C2×D991)⋊C3 |
| unambiguous semidirect product | (C2×C991⋊C3)⋊C2 |
| Fitting, socle | C2×C991 ⋊ C2×C3 |
| derived, Sylow | C991 ⋊ C22×C3 |
| Hall | C2×D991 ⋊ C3 |
| Hall | C991⋊C3 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D991⋊C3 |
| commutator, cosocle, hypocenter | C991 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C991 | C2×C3 |
| LCS | G ▷ C991 | |
| UCS | C1 ◁ C2 | |
20 conjugacy classes of subgroups.
342 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#22581945⋊C2, D3×D991⋊C3, C2×C3×D991⋊C3, … |
| maximal normal subgroup of | C2×#22581945⋊C2, C2×C3×D991⋊C3 |
| maximal quotient of | C2×#22581943⋊C2, D3×D991⋊C3, C2×C3×D991⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11892, 8);