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 | #6896 ⋊ C2 |
66 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 54 |
A minimal faithful permutation representation — 2 generators on 18 points:
(1,4,9,3,7,5,6,2,8)(11,13)(12,16)(14,15)(17,18);(2,4,7)(5,9,8)(10,18,17,16,14,13,12,11,15)Polycyclic presentation:
2,3^5|c^3=d,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 | #92264⋊C2, C2×#92264, C3×#92264, … |
| maximal normal subgroup of | #92264⋊C2, C2×#92264, C3×#92264, … |
| maximal quotient of | #11757568, C2×#92264, #13090628, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(486, 109);