Finite Group DatabasebetaFinite Group Databasebeta| order | 33252 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C17 · Schur multiplier (H2) = C2 |
| Fitting, socle, Hall | C22×C17×C163 ⋊ C3 |
| derived, Hall | C22×C163 ⋊ C3×C17 |
| Hall | C17×C163 ⋊ A4 |
| Sylow | C163 ⋊ A4×C17 |
| Hall | C22×C17 ⋊ C163⋊C3 |
| Sylow | C22 ⋊ C17×C163⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | C22⋊(C163⋊C3) |
| commutator, cosocle, hypocenter | C22×C163 | C3×C17 |
| Frattini | C1 | G |
| Fitting, socle | C22×C17×C163 | C3 |
| LCS | G ▷ C22×C163 | |
| UCS | C1 ◁ C17 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11084 |
3740 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33252, 32);