Finite Group DatabasebetaFinite Group Databasebeta| order | 29084 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic661⋊C11 |
| derived, Sylow | C661 ⋊ C4×C11 |
| Hall | C661⋊C11 ⋊ C4 |
| Hall | Dic661 ⋊ C11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D661⋊C11 |
| commutator, hypocenter | C661 | C4×C11 |
| Fitting, socle, cosocle | C2×C661 | C2×C11 |
| prime radical | C2×C661⋊C11 | C2 |
| LCS | G ▷ C661 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2644 |
Polycyclic presentation:
2,11,661,2|a^2=d,c^a=c^660,c^b=c^634104 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29084, 2);