Finite Group DatabasebetaFinite Group Databasebeta| order | 657 |
| isoclinism | isoclinic class of C73⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
| direct product | C3×C73⋊C3 |
| unambiguous semidirect product | C73⋊C32 |
| unambiguous semidirect product | (C3×C73)⋊C3 |
| Fitting, socle | C3×C73 ⋊ C3 |
| derived, Sylow | C73 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C73⋊C3 |
| commutator, cosocle, hypocenter | C73 | C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C73 | C3 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 219 |
81 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D73⋊C3, D3×C73⋊C3, C3⋊(D73⋊C3), … |
| maximal normal subgroup of | C3×D73⋊C3, D3×C73⋊C3, C3⋊(D73⋊C3), … |
| maximal quotient of | C2×C3×C73⋊C3, C9×C73⋊C3, C3×#10620321, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(657, 4);