Finite Group DatabasebetaFinite Group Databasebeta| order | 486 |
| isoclinism | isoclinic class of #92201 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, derived, Sylow | #6859 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | #6859 | C2 |
| Frattini | C33 | C3⋊D3 |
| socle | C32 | #272 |
| LCS | G ▷ #6859 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 81 |
A minimal faithful permutation representation — 3 generators on 36 points:
(2,5)(3,4)(6,7)(8,9)(11,14)(12,17)(13,21)(15,25)(16,23)(18,19)(20,32)(22,31)(24,29)(26,30)(27,35)(28,36)(33,34);(1,8,5,3,6,7,4,2,9)(10,20,17,13,19,18,21,12,32)(11,28,31,16,33,27,29,15,30)(14,26,25,24,35,34,23,22,36);(2,6,8)(5,9,7)(10,11,14)(12,15,26)(13,16,24)(17,30,25)(18,31,34)(19,33,22)(20,28,35)(21,29,23)(27,36,32)Polycyclic presentation:
2,3^5|c^3=e,b^a=b^2,c^a=c^2e^2,d^a=de^2f,e^a=e^2,f^a=f^2,c^b=cd,d^b=def,d^c=df22 conjugacy classes — view the full character table.
| maximal subgroup of | #92163⋊C2, C2×#92201, C3×#92201, … |
| maximal normal subgroup of | #92163⋊C2, C2×#92201, C3×#92201, … |
| maximal quotient of | #11757324, C2×#92201, #13090450, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(486, 46);