Finite Group DatabasebetaFinite Group Databasebeta| order | 14652 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | D11×#66526⋊C2 |
| unambiguous semidirect product | (C11×#66526⋊C2)⋊C2 |
| unambiguous semidirect product | (C11⋊(#66526⋊C2))⋊C2 |
| unambiguous semidirect product | (D11×#66526)⋊C2 |
| Fitting, socle, derived, Hall | C11×C37 ⋊ C22×C9 |
| Hall | C11×#66526 ⋊ C22 |
| Hall | D11×D37 ⋊ C9 |
| Hall | #66526 ⋊ C2×D11 |
| Sylow | C37 ⋊ C2×C9×D11 |
| Sylow | C11 ⋊ C2×#66526⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C11×C37 | C22×C9 |
| prime radical | D11×D37⋊C3 | C3 |
| cosocle | C11×C37⋊C3 | C22×C3 |
| LCS | G ▷ C11×C37 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 407 |
140 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14652, 68);