Finite Group DatabasebetaFinite Group Databasebeta| order | 486 |
| isoclinism | isoclinic class of #92209 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, derived, Sylow | #6868 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | #6868 | C2 |
| Frattini | C33 | C3⋊D3 |
| socle | C32 | #272 |
| LCS | G ▷ #6868 | |
| UCS | C1 | |
63 conjugacy classes of subgroups.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 81 |
A minimal faithful permutation representation — 3 generators on 36 points:
(2,4)(3,7)(5,6)(8,9)(11,15)(12,18)(13,14)(16,26)(17,28)(19,30)(20,22)(21,29)(23,25)(24,32)(27,31)(33,35)(34,36);(10,21,18,13,22,20,14,12,29)(11,33,32,23,19,27,17,16,34)(15,36,26,28,31,30,25,24,35);(1,9,4,7,6,5,3,2,8)(10,11,15)(12,19,31)(13,23,28)(14,17,25)(16,24,21)(18,27,30)(20,34,35)(22,33,36)(26,29,32)Polycyclic presentation:
2,3^5|b^3=d^2,c^3=f^2,b^a=b^2d,c^a=c^2f,d^a=d^2,e^a=ef^2,f^a=f^2,c^b=ce,e^b=ef30 conjugacy classes — view the full character table.
| maximal subgroup of | #92177⋊C2, C2×#92209, #13090510, … |
| maximal normal subgroup of | #92177⋊C2, C2×#92209, #13090510, … |
| maximal quotient of | #11757332, C2×#92209, #13090443, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(486, 54);