Finite Group DatabasebetaFinite Group Databasebeta| order | 32193 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C72 · Schur multiplier (H2) = C3×C7 |
| direct product | C3×C72×C73⋊C3 |
| unambiguous semidirect product | C73⋊(C32×C72) |
| unambiguous semidirect product | (C3×C73)⋊(C3×C72) |
| Fitting, socle | C3×C72×C73 ⋊ C3 |
| derived, Sylow | C73 ⋊ C32×C72 |
| Hall | C72×C73 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C72 | C73⋊C3 |
| commutator, cosocle, hypocenter | C73 | C32×C72 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C73 | C3 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C3×C72 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10731 |
3969 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32193, 41);