Finite Group DatabasebetaFinite Group Databasebeta| order | 486 |
| automorphism | Aut(G) = C3×D3×(C3⋊D3)⋊C3 (order 972) · Inn(G) = C3×(C3⋊D3)⋊C3 · Out(G) = C2×C3 |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, Sylow | C9⋊H(3,𝔽3) ⋊ C2 |
82 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 54 |
A minimal faithful permutation representation — 2 generators on 18 points:
(2,4)(3,6)(5,7)(8,9)(10,13,18,12,16,14,15,11,17);(1,2,8)(3,5,7)(4,6,9)(11,13,16)(14,18,17)Polycyclic presentation:
2,3^5|c^3=d,e^a=e^2,f^a=f^2,c^b=cd,e^b=ef42 conjugacy classes — view the full character table.
| maximal subgroup of | D9⋊((C3⋊D3)⋊C3), C2×#92262, #10624622⋊C2, … |
| maximal normal subgroup of | D9⋊((C3⋊D3)⋊C3), C2×#92262, C3×#92262, … |
| maximal quotient of | #11757566, C2×#92262, #13090622, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(486, 107);