Finite Group DatabasebetaFinite Group Databasebeta| order | 486 |
| isoclinism | isoclinic class of #92309 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C9 |
No aliases for this group.
| Fitting, Sylow | #6896 ⋊ C2 |
| derived | C92 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C92 | C2×C3 |
| Frattini, socle | C32 | C3×C3⋊D3 |
| Fitting | #6896 | C2 |
| LCS | G ▷ C92 | |
| UCS | C1 | |
84 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 81 |
A minimal faithful permutation representation — 3 generators on 18 points:
(2,6,9,4,5,8)(3,7)(11,17,18,13,14,15)(12,16);(10,14,13,12,18,15,16,11,17);(1,9,4,7,5,6,3,2,8)Polycyclic presentation:
2,3^5|c^3=e^2,d^3=f,c^a=c^2e,d^a=d^2f^2,e^a=e^2,f^a=f^2,c^b=ce,d^b=df30 conjugacy classes — view the full character table.
| derived subgroup of | #11757690⋊C2 |
| maximal subgroup of | #11757690, #92264⋊C2, #92308⋊C2, … |
| maximal normal subgroup of | #11757690, #92264⋊C2, #92308⋊C2, … |
| maximal quotient of | #11757613, C2×#92309, #13090629, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(486, 154);