Finite Group DatabasebetaFinite Group Databasebeta| order | 32193 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, derived, Hall | C49×C73 ⋊ C9 |
| Sylow | C73 ⋊ C49⋊C9 |
| Sylow | C49 ⋊ #10620323 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C49×C73 | C9 |
| Frattini | C7 | #17987164 |
| socle | C7×C73 | C7⋊C9 |
| prime radical | C7×C73⋊C3 | ΓL(1,𝔽8) |
| cosocle | C49×C73⋊C3 | C3 |
| LCS | G ▷ C49×C73 | |
| UCS | C1 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3577 |
Polycyclic presentation:
3^2,7,73,7|a^3=b^2,c^7=e^2,c^a=c^2e,d^a=d^4,e^a=e^2,d^b=d^8449 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32193, 9);