Finite Group DatabasebetaFinite Group Databasebeta| order | 33252 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C163⋊C3)⋊Dic17 |
| unambiguous semidirect product | Dic2771⋊C3 |
| derived, Hall | C17×C163 ⋊ C3×C4 |
| Hall | Dic2771 ⋊ C3 |
| Hall | C17×C163⋊C3 ⋊ C4 |
| Hall | C163⋊C3 ⋊ Dic17 |
| Sylow | C163 ⋊ C3×Dic17 |
| Sylow | C17 ⋊ (C163⋊C3)⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C17⋊(D163⋊C3) |
| commutator, hypocenter | C17×C163 | C3×C4 |
| Fitting, socle, cosocle | C2×C17×C163 | C2×C3 |
| prime radical | C2×C17×C163⋊C3 | C2 |
| LCS | G ▷ C17×C163 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11084 |
Polycyclic presentation:
2,3,17,163,2|a^2=e,c^a=c^16,d^a=d^162,d^b=d^104978 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33252, 12);