Finite Group DatabasebetaFinite Group Databasebeta| order | 14564 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic331⋊C11 |
| unambiguous semidirect product | (C331⋊C11)⋊C4 |
| derived, Sylow | C331 ⋊ C4×C11 |
| Hall | C331⋊C11 ⋊ C4 |
| Hall | Dic331 ⋊ C11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D331⋊C11 |
| commutator, hypocenter | C331 | C4×C11 |
| Fitting, socle, cosocle | C2×C331 | C2×C11 |
| prime radical | C2×C331⋊C11 | C2 |
| LCS | G ▷ C331 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1324 |
Polycyclic presentation:
2,11,331,2|a^2=d,c^a=c^330,c^b=c^27074 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14564, 2);