Finite Group DatabasebetaFinite Group Databasebeta| order | 486 |
| isoclinism | isoclinic class of #92299 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, Sylow | C9×3−1+2 ⋊ 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 | C9×3−1+2 | C2 |
| LCS | G ▷ C92 | |
| UCS | C1 | |
91 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 81 |
A minimal faithful permutation representation — 3 generators on 18 points:
(2,4)(3,7)(5,6)(8,9)(11,15,18,13,14,17)(12,16);(10,18,13,16,14,15,12,11,17);(1,9,4,7,6,5,3,2,8)Polycyclic presentation:
2,3^5|c^3=e^2,d^3=f^2,c^a=c^2e,d^a=d^2f,e^a=e^2,f^a=f^2,d^b=df54 conjugacy classes — view the full character table.
| maximal subgroup of | D9×AGL(1,ℤ/9), C2×#92299, (3−1+2⋊C27)⋊C2, … |
| maximal normal subgroup of | D9×AGL(1,ℤ/9), C2×#92299, C3×#92299, … |
| maximal quotient of | #11757603, C2×#92299, #13090609, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(486, 144);