Finite Group DatabasebetaFinite Group Databasebeta| order | 486 |
| isoclinism | isoclinic class of #92161 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, Sylow | #6857 ⋊ C2 |
| derived | C32⋊C9 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #4177 |
| commutator, cosocle, hypocenter | C32⋊C9 | C2×C3 |
| Frattini | C33 | C3×D3 |
| Fitting | #6857 | C2 |
| socle | C32 | (C3⋊D3)⋊C3 |
| LCS | G ▷ C32⋊C9 | |
| UCS | C1 ◁ C3 | |
59 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 18 |
A minimal faithful permutation representation — 2 generators on 18 points:
(1,7,4,2,3,11)(5,17,12,14,10,18)(6,16,13,8,9,15);(1,12,3,5,13,10,6,4,9)(2,16,11,8,17,15,14,7,18)Polycyclic presentation:
2,3^5|c^3=e,c^a=c^2e^2,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 | #92161⋊C2, C2×#92161, C3×#92161, … |
| maximal normal subgroup of | #92161⋊C2, C2×#92161, C3×#92161, … |
| maximal quotient of | #11757284, C2×#92161, #13090449, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(486, 6);