Finite Group DatabasebetaFinite Group Databasebeta| order | 32253 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C827 · Schur multiplier (H2) = C1 |
| direct product | C13⋊C3×C827 |
| unambiguous semidirect product | C13⋊(C3×C827) |
| unambiguous semidirect product | (C13×C827)⋊C3 |
| Fitting, socle, Hall | C13×C827 ⋊ C3 |
| derived, Sylow | C13 ⋊ C3×C827 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C827 | C13⋊C3 |
| commutator, cosocle, hypocenter | C13 | C3×C827 |
| Frattini | C1 | G |
| Fitting, socle | C13×C827 | C3 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C827 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10751 |
5789 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32253, 1);