Finite Group DatabasebetaFinite Group Databasebeta| order | 486 |
| isoclinism | isoclinic class of #92302 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, Sylow | #6891 ⋊ C2 |
| derived | C32⋊C9 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊AGL(1,ℤ/9) |
| commutator, cosocle, hypocenter | C32⋊C9 | C2×C3 |
| Frattini, socle | C32 | C3×C3⋊D3 |
| Fitting | #6891 | C2 |
| LCS | G ▷ C32⋊C9 | |
| UCS | C1 ◁ C3 | |
147 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 18 |
A minimal faithful permutation representation — 3 generators on 18 points:
(1,2)(3,15,11,8,9,17)(4,12)(5,7)(6,10,16,13,14,18);(3,9,11)(6,16,14)(8,17,15)(10,18,13);(1,11,13,5,9,10,4,3,18)(2,16,8,12,14,15,7,6,17)Polycyclic presentation:
2,3^5|c^3=e^2,c^a=c^2e,d^a=d^2,e^a=e^2,c^b=ce,d^c=df39 conjugacy classes — view the full character table.
| maximal subgroup of | (((C3⋊D3)⋊C9)⋊C2)⋊C3, C2×#92302, #13090732, … |
| maximal normal subgroup of | (((C3⋊D3)⋊C9)⋊C2)⋊C3, C2×#92302, #13090732, … |
| maximal quotient of | #11757606, C2×#92302, #13090620, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(486, 147);