Finite Group DatabasebetaFinite Group Databasebeta| order | 32193 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C49 · Schur multiplier (H2) = C1 |
| direct product | C49×#10620323 |
| Fitting, Hall | C49×C73 ⋊ C9 |
| derived, Sylow | C73 ⋊ C9×C49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C49 | #10620323 |
| commutator, hypocenter | C73 | C9×C49 |
| Frattini | C7 | C7×#10620323 |
| Fitting | C49×C73 | C9 |
| socle | C7×C73 | C7×C9 |
| prime radical, cosocle | C7×C73⋊C3 | C3×C7 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C49 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3577 |
833 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32193, 7);