Finite Group DatabasebetaFinite Group Databasebeta| order | 486 |
| isoclinism | isoclinic class of #92213 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, derived, Sylow | #6872 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | #6872 | C2 |
| Frattini | C3×C9 | C3⋊D3 |
| socle | C3 | #4181 |
| LCS | G ▷ #6872 | |
| 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)(16,45)(17,46)(19,26)(20,43)(22,51)(23,30)(25,56)(27,52)(28,60)(29,61)(31,32)(33,55)(35,48)(36,44)(38,42)(40,66)(41,69)(47,73)(49,64)(50,62)(53,77)(54,72)(57,59)(58,80)(63,76)(65,71)(67,70)(68,74)(75,79)(78,81);(1,3,12)(2,8,26)(4,13,36)(5,14,38)(6,19,24)(7,22,52)(9,27,51)(10,33,64)(11,28,35)(15,44,39)(16,40,65)(17,41,67)(18,42,37)(20,47,54)(21,49,55)(23,53,76)(25,57,32)(29,58,68)(30,63,77)(31,59,56)(34,48,60)(43,72,73)(45,71,66)(46,70,69)(50,75,78)(61,74,80)(62,81,79);(1,43,34,46,31,23,4,2,61,18,62,21,16,9,7,45,10,50,5,29,6,15,30,32,17,11,20)(3,72,49,70,59,22,13,8,75,42,81,19,40,27,25,71,33,47,14,58,48,44,63,53,41,28,74)(12,68,60,69,77,76,36,35,80,37,73,55,65,56,52,66,26,78,38,79,24,39,51,57,67,64,54)Polycyclic presentation:
2,3^5|b^3=d^2f^2,d^3=f,b^a=b^2d,c^a=c^2,d^a=d^2f^2,f^a=f^2,c^b=ce,e^b=ef,e^c=ef^230 conjugacy classes — view the full character table.
| maximal subgroup of | #92181⋊C2, C2×#92213, C3×#92213, … |
| maximal normal subgroup of | #92181⋊C2, C2×#92213, C3×#92213, … |
| maximal quotient of | #11757336, C2×#92213, #13090445, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(486, 58);