Finite Group DatabasebetaFinite Group Databasebeta| order | 486 |
| isoclinism | isoclinic class of #92159 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, Sylow | #6856 ⋊ C2 |
| derived | C3×H(3,𝔽3) ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #4175 |
| commutator, cosocle, hypocenter | C3×H(3,𝔽3) | C2×C3 |
| Frattini | C33 | C3×D3 |
| Fitting | #6856 | C2 |
| socle | C32 | (C3⋊D3)⋊C3 |
| LCS | G ▷ C3×H(3,𝔽3) | |
| UCS | C1 ◁ C3 | |
73 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 54 |
A minimal faithful permutation representation — 2 generators on 18 points:
(1,2,4)(3,6,8,7,5,9)(11,17,16,14,15,18);(2,5,6)(10,11,14)(12,16,18)(13,15,17)Polycyclic presentation:
2,3^5|c^a=c^2,d^a=d^2f,e^a=e^2,c^b=cd,d^b=de,d^c=df31 conjugacy classes — view the full character table.
| maximal subgroup of | #92159⋊C2, C2×#92159, C3⋊#92159, … |
| maximal normal subgroup of | #92159⋊C2, C2×#92159, C3×#92159, … |
| maximal quotient of | #11757282, C2×#92159, #13090448, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(486, 4);