Finite Group DatabasebetaFinite Group Databasebeta| order | 11524 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D43×D67 |
| unambiguous semidirect product | (C67×D43)⋊C2 |
| unambiguous semidirect product | (C43×D67)⋊C2 |
| unambiguous semidirect product | D2881⋊C2 |
| Fitting, socle, derived, Hall | C43×C67 ⋊ C22 |
| Sylow | C67 ⋊ C2×D43 |
| Sylow | C43 ⋊ C2×D67 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C43×C67 | C22 |
| LCS | G ▷ C43×C67 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
805 conjugacy classes — view the full character table.
| maximal subgroup of | #31772251⋊C2, #31772250⋊C2, D67×D43⋊C3, … |
| maximal normal subgroup of | #31772251⋊C2, #31772250⋊C2, D67×D43⋊C3, … |
| maximal quotient of | C3×D43×D67, D67×D129, D43×D201, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11524, 6);