Finite Group DatabasebetaFinite Group Databasebeta| order | 486 |
| isoclinism | isoclinic class of #92214 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, derived, Sylow | #6873 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | #6873 | C2 |
| Frattini | C3×C9 | C3⋊D3 |
| socle | C3 | #4181 |
| LCS | G ▷ #6873 | |
| UCS | C1 | |
46 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 81 |
A minimal faithful permutation representation — 3 generators on 81 points:
(2,6)(3,12)(4,15)(5,18)(7,9)(8,24)(10,21)(11,34)(13,39)(14,37)(16,17)(19,26)(20,43)(22,51)(23,30)(25,57)(27,53)(28,61)(29,50)(31,32)(33,56)(35,48)(36,44)(38,42)(40,68)(41,66)(45,46)(47,73)(49,64)(52,67)(54,79)(55,72)(58,60)(59,80)(62,65)(63,78)(69,74)(70,71)(75,76)(77,81);(1,3,12)(2,8,26)(4,13,36)(5,14,38)(6,19,24)(7,22,53)(9,27,51)(10,33,64)(11,28,35)(15,44,39)(16,40,66)(17,41,68)(18,42,37)(20,47,55)(21,49,56)(23,54,78)(25,58,32)(29,59,76)(30,63,79)(31,60,57)(34,48,61)(43,72,73)(45,52,70)(46,71,67)(50,75,80)(62,77,69)(65,74,81);(1,43,21,45,30,32,4,2,50,5,62,34,16,9,7,17,11,65,18,29,6,15,31,23,46,10,20)(3,72,19,52,63,54,13,8,47,14,77,49,40,27,25,41,28,75,42,59,48,44,60,22,71,33,74)(12,69,56,70,51,58,36,35,80,38,76,61,66,57,53,68,64,81,37,73,24,39,79,78,67,26,55)Polycyclic presentation:
2,3^5|b^3=d^2f,d^3=f^2,b^a=b^2d,c^a=c^2,d^a=d^2f,f^a=f^2,c^b=ce,e^b=ef,e^c=ef^230 conjugacy classes — view the full character table.
| maximal subgroup of | #92183⋊C2, C2×#92214, C3×#92214, … |
| maximal normal subgroup of | #92183⋊C2, C2×#92214, C3×#92214, … |
| maximal quotient of | #11757337, C2×#92214, #13090445, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(486, 59);