Finite Group DatabasebetaFinite Group Databasebeta| order | 11868 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| Fitting, socle, derived, Hall | C23×C43 ⋊ C22×C3 |
| Hall | D23×D43 ⋊ C3 |
| Hall | C23×C43⋊C3 ⋊ C22 |
| Hall | C43⋊C3 ⋊ C2×D23 |
| Sylow | C43 ⋊ C2×C3×D23 |
| Sylow | C23 ⋊ C2×D43⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C23×C43 | C22×C3 |
| LCS | G ▷ C23×C43 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
169 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D23×D43⋊C3, D69×D43⋊C3, D23×C3⋊(D43⋊C3), … |
| maximal normal subgroup of | C3×D23×D43⋊C3 |
| maximal quotient of | D23×D43⋊C9, C3×D23×D43⋊C3, D69×D43⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11868, 14);