Finite Group DatabasebetaFinite Group Databasebeta| order | 657 |
| isoclinism | isoclinic class of C73⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C73 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C73⋊C3 |
| commutator, hypocenter | C73 | C9 |
| Fitting, socle, prime radical, cosocle | C3×C73 | C3 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C3 | |
6 conjugacy classes of subgroups.
| minimal degree | μ(G) = 82 |
| transitive degree | μt(G) = 657 |
Polycyclic presentation:
3^2,73|a^3=b,c^a=c^881 conjugacy classes — view the full character table.
| maximal subgroup of | #10620321⋊C2, C2×#10620321, C9×C73⋊C3, … |
| maximal normal subgroup of | #10620321⋊C2, C2×#10620321, C9×C73⋊C3, … |
| maximal quotient of | C2×#10620321, #14520291, C3×#10620321, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(657, 1);