Finite Group DatabasebetaFinite Group Databasebeta| order | 486 |
| isoclinism | isoclinic class of D3×H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33 · Schur multiplier (H2) = C32 |
| direct product | C3×D3×3−1+2 |
| unambiguous semidirect product | C3⋊(C2×C3×3−1+2) |
| unambiguous semidirect product | (D3×C9)⋊C32 |
| Fitting, Sylow | C32×3−1+2 ⋊ C2 |
258 conjugacy classes of subgroups.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 54 |
A minimal faithful permutation representation — 3 generators on 15 points:
(5,6)(8,11,12)(10,14,15);(4,5,6)(7,8,10,9,12,14,13,11,15);(1,2,3)99 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(486, 225);