Finite Group DatabasebetaFinite Group Databasebeta| order | 486 |
| isoclinism | isoclinic class of #92161 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, Sylow | #6861 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #4177 |
| commutator, cosocle, hypocenter | C32⋊C9 | C2×C3 |
| Frattini | C33 | C3×D3 |
| Fitting | #6861 | C2 |
| socle | C32 | (C3⋊D3)⋊C3 |
| prime radical | #4181 | C3 |
| LCS | G ▷ C32⋊C9 | |
| UCS | C1 ◁ C3 | |
35 conjugacy classes of subgroups.
| minimal degree | μ(G) = 54 |
| transitive degree | μt(G) = 54 |
A minimal faithful permutation representation — 2 generators on 54 points:
(1,21,27,9,13,19,5,7,28,2,12,40,6,34,10,18,3,41)(4,44,26,24,32,49,16,29,48,14,33,46,17,51,30,35,11,54)(8,42,52,38,45,50,36,31,43,22,20,47,25,37,39,15,23,53);(1,16,22,5,17,15,6,4,38)(2,25,14,9,36,24,18,8,35)(3,32,42,13,33,31,12,11,37)(7,45,29,21,23,44,34,20,51)(10,48,50,27,30,47,28,26,53)(19,43,46,41,52,49,40,39,54)Polycyclic presentation:
2,3^5|b^3=f,c^3=e,c^a=c^2e^2,d^a=d^2f,e^a=e^2,c^b=cd,d^b=de,d^c=df31 conjugacy classes — view the full character table.
| maximal subgroup of | #92165⋊C2, C2×#92165, C3×#92165, … |
| maximal normal subgroup of | #92165⋊C2, C2×#92165, C3×#92165, … |
| maximal quotient of | #11757288, C2×#92165, #13090451, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(486, 10);