Finite Group DatabasebetaFinite Group Databasebeta| order | 486 |
| isoclinism | isoclinic class of #4175 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, Sylow | #6866 ⋊ C2 |
| derived | C33 ⋊ C2×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #4175 |
| commutator, hypocenter | C33 | C2×C9 |
| Frattini | C33 | C3×D3 |
| Fitting | #6866 | C2 |
| socle | C32 | (C3⋊D3)⋊C3 |
| prime radical | C3×C3⋊(C3⋊D3) | C3 |
| cosocle | C34 | C2×C3 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C3 | |
87 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 18 |
A minimal faithful permutation representation — 2 generators on 18 points:
(1,13,16,7,10,12,5,6,15,2,9,18,4,14,8,11,3,17);(3,10,9)(6,13,14)Polycyclic presentation:
2,3^5|b^3=c,d^a=d^2,e^a=e^2,f^a=f^2,d^b=de,e^b=ef39 conjugacy classes — view the full character table.
| maximal subgroup of | #92173⋊C2, C2×#92173, #13090499, … |
| maximal normal subgroup of | #92173⋊C2, C2×#92173, C3×#92173, … |
| maximal quotient of | #11757296, C2×#92173, #13090435, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(486, 18);