Finite Group DatabasebetaFinite Group Databasebeta| order | 486 |
| isoclinism | isoclinic class of #92159 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, Sylow | #6857 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #4175 |
| commutator, cosocle, hypocenter | C3×H(3,𝔽3) | C2×C3 |
| Frattini | C33 | C3×D3 |
| Fitting | #6857 | C2 |
| socle | C32 | (C3⋊D3)⋊C3 |
| prime radical | C3⋊#272 | C3 |
| LCS | G ▷ C3×H(3,𝔽3) | |
| UCS | C1 ◁ C3 | |
59 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 18 |
A minimal faithful permutation representation — 2 generators on 18 points:
(1,16,4,8,10,14,13,6,17,2,11,12,5,15,9,7,3,18);(1,4,3)(2,6,12)(5,9,11)(7,15,18)(8,16,14)(10,13,17)Polycyclic presentation:
2,3^5|b^3=f,c^a=c^2,d^a=d^2f^2,e^a=e^2,c^b=cd,d^b=de,d^c=df^231 conjugacy classes — view the full character table.
| maximal subgroup of | #92161⋊C2, C2×#92162, C3×#92162, … |
| maximal normal subgroup of | #92161⋊C2, C2×#92162, C3×#92162, … |
| maximal quotient of | #11757285, C2×#92162, #13090448, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(486, 7);