Finite Group DatabasebetaFinite Group Databasebeta| order | 32193 |
| automorphism | ? |
| homology | Abelianization (H1) = C7×C9 · Schur multiplier (H2) = C1 |
| direct product | C7×#17987164 |
| Fitting, socle, Hall | C72×C73 ⋊ C9 |
| derived | C7×C73 ⋊ C7×C9 |
| Sylow | C73 ⋊ C7×C7⋊C9 |
| Sylow | C72 ⋊ #10620323 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | #17987164 |
| commutator, hypocenter | C7×C73 | C7×C9 |
| Frattini | C1 | G |
| Fitting, socle | C72×C73 | C9 |
| prime radical | C72×C73⋊C3 | C3 |
| cosocle | C7×C73⋊C3 | C3×C7 |
| LCS | G ▷ C7×C73 | |
| UCS | C1 ◁ C7 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1533 |
497 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32193, 28);