Finite Group DatabasebetaFinite Group Databasebeta| order | 486 |
| isoclinism | isoclinic class of #92302 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #6895⋊C2 |
| Fitting, Sylow | #6895 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊AGL(1,ℤ/9) |
| commutator, cosocle, hypocenter | C32⋊C9 | C2×C3 |
| Frattini, socle | C32 | C3×C3⋊D3 |
| Fitting | #6895 | C2 |
| prime radical | #4181 | C3 |
| LCS | G ▷ C32⋊C9 | |
| UCS | C1 ◁ C3 | |
72 conjugacy classes of subgroups.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 54 |
A minimal faithful permutation representation — 3 generators on 36 points:
(2,6,9,4,5,8)(3,7)(10,16,32,13,26,14,20,11,22)(12,33,30,27,24,29,18,23,31,17,25,36,19,34,21,28,15,35);(12,18,19)(15,24,25)(17,27,28)(21,30,31)(23,33,34)(29,35,36);(1,9,4,7,5,6,3,2,8)(10,12,17)(11,15,23)(13,19,27)(14,21,29)(16,25,33)(18,28,20)(22,31,35)(24,34,26)(30,36,32)Polycyclic presentation:
2,3^5|b^3=f,c^3=e^2,c^a=c^2e,d^a=d^2,e^a=e^2,c^b=ce,d^c=df39 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(486, 152);