Finite Group DatabasebetaFinite Group Databasebeta| order | 32949 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C7×C523 ⋊ C9 |
| Sylow | C523 ⋊ C7⋊C9 |
| Sylow | C7 ⋊ #17989922 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C523 | C9 |
| prime radical, cosocle | C7×C523⋊C3 | C3 |
| LCS | G ▷ C7×C523 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3661 |
Polycyclic presentation:
3^2,7,523|a^3=b^2,c^a=c^2,d^a=d^468,d^b=d^60421 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32949, 9);