Finite Group DatabasebetaFinite Group Databasebeta| order | 32428 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C121 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic67⋊C121 |
| unambiguous semidirect product | (C67⋊C121)⋊C4 |
| derived, Sylow | C67 ⋊ C4×C121 |
| Hall | C67⋊C121 ⋊ C4 |
| Hall | Dic67 ⋊ C121 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C11 | D67⋊C11 |
| commutator, hypocenter | C67 | C4×C121 |
| Fitting, socle, prime radical, cosocle | C2×C11×C67 | C2×C11 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C2×C11 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 32428 |
Polycyclic presentation:
2,11,67,2,11|a^2=d,b^11=e,c^a=c^66,c^b=c^64550 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32428, 2);