Finite Group DatabasebetaFinite Group Databasebeta| order | 32193 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3×C7 |
| direct product | #3862×C73⋊C3 |
| Fitting, socle, derived, Hall | C72×C73 ⋊ C32 |
| Sylow | C73 ⋊ C3×#3862 |
| Sylow | C72 ⋊ C3×C73⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72×C73 | C32 |
| LCS | G ▷ C72×C73 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1533 |
513 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32193, 40);