Finite Group DatabasebetaFinite Group Databasebeta| order | 486 |
| isoclinism | isoclinic class of #4169 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, Sylow | #6855 ⋊ C2 |
| derived | C3×C9 ⋊ C2×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #4169 |
| commutator, hypocenter | C3×C9 | C2×C9 |
| Frattini, socle | C33 | C3×D3 |
| Fitting | #6855 | C2 |
| prime radical | C3×C3⋊D9 | C3 |
| cosocle | C32×C9 | C2×C3 |
| LCS | G ▷ C3×C9 | |
| UCS | C1 ◁ C3 | |
69 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 54 |
A minimal faithful permutation representation — 2 generators on 27 points:
(1,5,9,3,8,4,6,2,7)(11,16,18,13,14,17)(12,15)(20,22)(21,25)(23,24)(26,27);(10,11,13)(12,14,17)(15,18,16)(19,27,22,25,24,23,21,20,26)Polycyclic presentation:
2,3^5|b^3=c,d^3=f^2,d^a=d^2f,e^a=e^2,f^a=f^2,d^b=de63 conjugacy classes — view the full character table.
| maximal subgroup of | #92158⋊C2, C2×#92158, #13090510, … |
| maximal normal subgroup of | #92158⋊C2, C2×#92158, C3×#92158, … |
| maximal quotient of | #11757281, C2×#92158, #13090480, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(486, 3);