Finite Group DatabasebetaFinite Group Databasebeta| order | 32274 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9×C11 · Schur multiplier (H2) = C1 |
| direct product | C2×C11×#13091814 |
| Fitting, socle, Hall | C2×C11×C163 ⋊ C9 |
| derived, Sylow | C163 ⋊ C2×C9×C11 |
| Hall | C11×C163 ⋊ C2×C9 |
| Hall | C2×C163 ⋊ C9×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11 | #13091814 |
| commutator, hypocenter | C163 | C2×C9×C11 |
| Frattini | C1 | G |
| Fitting, socle | C2×C11×C163 | C9 |
| prime radical | C2×C11×C163⋊C3 | C3 |
| cosocle | C163⋊C3 | C2×C3×C11 |
| LCS | G ▷ C163 | |
| UCS | C1 ◁ C2×C11 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3586 |
594 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32274, 17);