Finite Group DatabasebetaFinite Group Databasebeta| order | 486 |
| isoclinism | isoclinic class of D9⋊H(3,𝔽3) |
| automorphism | Aut(G) = C3×D3×AGL(1,ℤ/9) (order 972) · Inn(G) = C3×AGL(1,ℤ/9) · Out(G) = C2×C3 |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, Sylow | #6900 ⋊ C2 |
71 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 18 |
A minimal faithful permutation representation — 2 generators on 18 points:
(1,17,5,14,9,16,4,7,12,2,11,13,6,15,10,8,3,18);(1,12,11,4,10,3,6,5,9)(2,17,18,14,15,13,8,7,16)Polycyclic presentation:
2,3^5|c^3=d^2,e^3=f^2,e^a=e^2f,f^a=f^2,c^b=cd,e^b=ef42 conjugacy classes — view the full character table.
| maximal subgroup of | #92265⋊C2, C2×#92265, #92191⋊C3, … |
| maximal normal subgroup of | #92265⋊C2, C2×#92265, C3×#92265, … |
| maximal quotient of | #11757569, C2×#92265, #13090635, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(486, 110);