Finite Group DatabasebetaFinite Group Databasebeta| order | 486 |
| isoclinism | isoclinic class of #92160 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, Sylow | #6856 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #4179 |
| commutator, cosocle, hypocenter | C32⋊C9 | C2×C3 |
| Frattini | C33 | C3×D3 |
| Fitting | #6856 | C2 |
| socle | C32 | (C3⋊D3)⋊C3 |
| LCS | G ▷ C32⋊C9 | |
| UCS | C1 ◁ C3 | |
46 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 18 |
A minimal faithful permutation representation — 2 generators on 18 points:
(1,17,4,8,11,15,5,7,13,2,10,12,6,18,9,14,3,16);(1,9,3,6,13,10,5,4,11)(2,18,12,14,17,16,8,7,15)Polycyclic presentation:
2,3^5|b^3=f,c^3=e^2,c^a=c^2e,d^a=d^2f,e^a=e^2,c^b=cd,d^b=de,d^c=df31 conjugacy classes — view the full character table.
| maximal subgroup of | #92160⋊C2, C2×#92160, C3⋊#92160, … |
| maximal normal subgroup of | #92160⋊C2, C2×#92160, C3×#92160, … |
| maximal quotient of | #11757283, C2×#92160, #13090454, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(486, 5);