Finite Group DatabasebetaFinite Group Databasebeta| order | 32193 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3×C7 |
| direct product | C3×C73⋊#3862 |
| unambiguous semidirect product | (C3×C73)⋊#3862 |
| Fitting, socle | C3×C72×C73 ⋊ C3 |
| derived, Hall | C72×C73 ⋊ C32 |
| Sylow | C73 ⋊ C3×#3862 |
| Sylow | C72 ⋊ C3×C73⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C73⋊#3862 |
| commutator, cosocle, hypocenter | C72×C73 | C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C73 | C3 |
| LCS | G ▷ C72×C73 | |
| UCS | C1 ◁ C3 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4599 |
3585 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32193, 49);