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 | #6896 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #4207 |
| commutator, cosocle, hypocenter | C32⋊C9 | C2×C3 |
| Frattini, socle | C32 | C3×C3⋊D3 |
| Fitting | #6896 | C2 |
| prime radical | #4181 | C3 |
| LCS | G ▷ C32⋊C9 | |
| UCS | C1 ◁ C3 | |
63 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 18 |
A minimal faithful permutation representation — 3 generators on 18 points:
(1,15,4,8,10,14,13,6,17,2,11,12,5,16,9,7,3,18);(3,10,11)(4,9,17)(6,15,16)(12,18,14);(1,17,3,13,9,10,5,4,11)(2,15,12,8,16,14,7,6,18)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=df^239 conjugacy classes — view the full character table.
| maximal subgroup of | #92308⋊C2, C2×#92308, C3×#92308, … |
| maximal normal subgroup of | #92308⋊C2, C2×#92308, C3×#92308, … |
| maximal quotient of | #11757612, C2×#92308, #13090630, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(486, 153);