Finite Group DatabasebetaFinite Group Databasebeta| order | 32193 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | #3861⋊(C73⋊C3) |
| Fitting, socle, derived, Hall | C72×C73 ⋊ C32 |
| Sylow | C73 ⋊ ΓL(1,𝔽8)2 |
| 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 |
Polycyclic presentation:
3^2,7^2,73|c^a=c^4,e^a=e^8,c^b=c^2,d^b=d^2481 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32193, 33);