Finite Group DatabasebetaFinite Group Databasebeta| order | 32252 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×Dic733 |
| derived, Sylow | C733 ⋊ C4×C11 |
| Hall | C11×C733 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11 | D733 |
| commutator, hypocenter | C733 | C4×C11 |
| Frattini | C2 | C11×D733 |
| Fitting, socle, prime radical | C2×C11×C733 | C2 |
| cosocle | C2×C733 | C2×C11 |
| LCS | G ▷ C733 | |
| UCS | C1 ◁ C2×C11 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 32252 |
8096 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32252, 3);