Finite Group DatabasebetaFinite Group Databasebeta| order | 486 |
| isoclinism | isoclinic class of #92198 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C32 |
No aliases for this group.
| Fitting, derived, Sylow | #6856 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | #6856 | C2 |
| Frattini | C33 | C3⋊D3 |
| socle | C32 | #272 |
| LCS | G ▷ #6856 | |
| UCS | C1 | |
94 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 81 |
A minimal faithful permutation representation — 3 generators on 18 points:
(2,5)(3,4)(6,9)(7,8)(11,14)(12,13)(15,18)(16,17);(2,6,7)(5,8,9)(10,11,14)(12,16,18)(13,15,17);(1,2,5)(3,6,8)(4,7,9)(11,15,16)(14,17,18)Polycyclic presentation:
2,3^5|b^a=b^2,c^a=c^2,d^a=de^2,e^a=e^2,f^a=f^2,c^b=cd,d^b=def,d^c=df^222 conjugacy classes — view the full character table.
| derived subgroup of | #11757370⋊C2 |
| maximal subgroup of | #11757370, #92160⋊C2, #92159⋊C2, … |
| maximal normal subgroup of | #11757370, #92160⋊C2, #92159⋊C2, … |
| maximal quotient of | #11757321, C2×#92198, #13090450, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(486, 43);