Finite Group DatabasebetaFinite Group Databasebeta| order | 486 |
| isoclinism | isoclinic class of #92208 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, derived, Sylow | #6867 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | #6867 | C2 |
| Frattini | C33 | C3⋊D3 |
| socle | C32 | #272 |
| LCS | G ▷ #6867 | |
| 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)(19,31)(20,21)(22,30)(23,25)(24,34)(27,36)(29,32)(33,35);(10,22,18,14,21,20,13,12,30)(11,19,34,17,33,27,23,16,29)(15,32,26,25,36,35,28,24,31);(1,9,4,7,6,5,3,2,8)(10,11,15)(12,19,32)(13,23,28)(14,17,25)(16,24,21)(18,29,31)(20,34,26)(22,33,36)(27,35,30)Polycyclic presentation:
2,3^5|b^3=d^2,c^3=f,b^a=b^2d,c^a=c^2f^2,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 | #92175⋊C2, C2×#92208, #13090504, … |
| maximal normal subgroup of | #92175⋊C2, C2×#92208, #13090504, … |
| maximal quotient of | #11757331, C2×#92208, #13090440, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(486, 53);