Finite Group DatabasebetaFinite Group Databasebeta| order | 663 |
| isoclinism | isoclinic class of C13⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×C13⋊C3 |
| unambiguous semidirect product | C13⋊(C3×C17) |
| unambiguous semidirect product | (C13×C17)⋊C3 |
| Fitting, socle, Hall | C13×C17 ⋊ C3 |
| derived, Sylow | C13 ⋊ C3×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | C13⋊C3 |
| commutator, cosocle, hypocenter | C13 | C3×C17 |
| Frattini | C1 | G |
| Fitting, socle | C13×C17 | C3 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C17 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 221 |
119 conjugacy classes — view the full character table.
| maximal subgroup of | D17×C13⋊C3, C17×D13⋊C3, C17⋊(D13⋊C3), … |
| maximal normal subgroup of | D17×C13⋊C3, C17×D13⋊C3, C17⋊(D13⋊C3), … |
| maximal quotient of | C2×C17×C13⋊C3, C17×C13⋊C9, C3×C17×C13⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(663, 1);