Finite Group DatabasebetaFinite Group Databasebeta| order | 486 |
| isoclinism | isoclinic class of #92304 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, Sylow | #6898 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #4207 |
| commutator, cosocle, hypocenter | C32⋊C9 | C2×C3 |
| Frattini, socle | C32 | C3×C3⋊D3 |
| Fitting | #6898 | C2 |
| prime radical | #4181 | C3 |
| LCS | G ▷ C32⋊C9 | |
| UCS | C1 ◁ C3 | |
58 conjugacy classes of subgroups.
| minimal degree | μ(G) = 54 |
| transitive degree | μt(G) = 54 |
A minimal faithful permutation representation — 3 generators on 54 points:
(1,26,4,10,15,23,22,7,31,2,13,14,6,25,11,9,3,36)(5,41,33,43,12,38,44,40,19,17,37,54,21,32,16,42,18,46)(8,34,51,50,28,49,29,48,35,20,24,47,30,45,52,53,27,39);(1,5,20)(2,8,17)(3,12,34)(4,16,39)(6,21,50)(7,24,32)(9,29,42)(10,30,43)(11,19,47)(13,18,45)(14,35,38)(15,37,48)(22,44,53)(23,51,46)(25,27,41)(26,28,40)(31,33,49)(36,52,54);(1,31,3,22,11,15,6,4,13)(2,26,14,10,25,23,9,7,36)(5,16,37,44,33,18,21,19,12)(8,27,52,30,24,35,29,28,51)(17,32,46,43,40,54,42,41,38)(20,47,45,53,39,34,50,49,48)Polycyclic presentation:
2,3^5|b^3=f,c^3=e^2,c^a=c^2e,d^a=d^2,e^a=e^2,d^b=de,d^c=df39 conjugacy classes — view the full character table.
| maximal subgroup of | #92311⋊C2, C2×#92311, C3×#92311, … |
| maximal normal subgroup of | #92311⋊C2, C2×#92311, C3×#92311, … |
| maximal quotient of | #11757615, C2×#92311, #13090633, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(486, 156);