Finite Group DatabasebetaFinite Group Databasebeta| order | 486 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, Sylow | #6891 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center | C3 | C3×(C3⋊D3)⋊C3 |
| commutator, cosocle | C33 | C2×C32 |
| Frattini, socle | C32 | C32×D3 |
| Fitting | #6891 | C2 |
| prime radical | C32×C3⋊D3 | C3 |
| hypercenter | C32 | (C3⋊D3)⋊C3 |
| hypocenter | C32 | C2×3−1+2 |
| LCS | G ▷ C33 ▷ C32 | |
| UCS | C1 ◁ C3 ◁ C32 | |
108 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 18 |
A minimal faithful permutation representation — 2 generators on 18 points:
(1,2)(3,13,10,6,9,14)(4,7)(5,11)(8,17,16,12,15,18);(1,9,16,4,3,8,5,10,15)(2,6,18,7,14,12,11,13,17)Polycyclic presentation:
2,3^5|b^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 | (((C3⋊D3)⋊C9)⋊C2)⋊C3, C2×#92259, #10624475⋊C2, … |
| maximal normal subgroup of | (((C3⋊D3)⋊C9)⋊C2)⋊C3, C2×#92259, #13091033, … |
| maximal quotient of | #11757563, C2×#92259, #13090617, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(486, 104);