Finite Group DatabasebetaFinite Group Databasebeta| order | 657 |
| isoclinism | isoclinic class of #10620323 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C73 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C73 | C9 |
| prime radical, cosocle | C73⋊C3 | C3 |
| LCS | G ▷ C73 | |
| UCS | C1 | |
6 conjugacy classes of subgroups.
| minimal degree | μ(G) = 73 |
| transitive degree | μt(G) = 73 |
Polycyclic presentation:
3^2,73|a^3=b,c^a=c^2,c^b=c^817 conjugacy classes — view the full character table.
| maximal subgroup of | #10620323⋊C2, C2×#10620323, C3×#10620323, … |
| maximal normal subgroup of | #10620323⋊C2, C2×#10620323, C3×#10620323, … |
| maximal quotient of | C2×#10620323, #14520299, C3×#10620323, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(657, 3);