Finite Group DatabasebetaFinite Group Databasebeta| order | 549 |
| isoclinism | isoclinic class of C61⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
| direct product | C3×C61⋊C3 |
| unambiguous semidirect product | C61⋊C32 |
| unambiguous semidirect product | (C3×C61)⋊C3 |
| Fitting, socle | C3×C61 ⋊ C3 |
| derived, Sylow | C61 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C61⋊C3 |
| commutator, cosocle, hypocenter | C61 | C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C61 | C3 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 183 |
69 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D61⋊C3, D3×C61⋊C3, C3⋊(D61⋊C3), … |
| maximal normal subgroup of | C3×D61⋊C3, D3×C61⋊C3, C3⋊(D61⋊C3), … |
| maximal quotient of | C2×C3×C61⋊C3, C9×C61⋊C3, C3×C61⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(549, 3);