Finite Group DatabasebetaFinite Group Databasebeta| order | 32193 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C7 |
No aliases for this group.
| Fitting, socle, derived, Hall | C72×C73 ⋊ C9 |
| Sylow | C73 ⋊ #89205 |
| Sylow | C72 ⋊ #10620323 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C72×C73 | C9 |
| prime radical, cosocle | C72×C73⋊C3 | C3 |
| LCS | G ▷ C72×C73 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1533 |
Polycyclic presentation:
3^2,7^2,73|a^3=b,c^a=c^2,d^a=d^4,e^a=e^2,e^b=e^8449 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32193, 39);