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 | #6859 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #4175 |
| commutator, cosocle, hypocenter | C3×H(3,𝔽3) | C2×C3 |
| Frattini | C33 | C3×D3 |
| Fitting | #6859 | C2 |
| socle | C32 | (C3⋊D3)⋊C3 |
| prime radical | C3⋊#272 | C3 |
| LCS | G ▷ C3×H(3,𝔽3) | |
| UCS | C1 ◁ C3 | |
54 conjugacy classes of subgroups.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 54 |
A minimal faithful permutation representation — 2 generators on 36 points:
(1,2,4)(3,6,8,7,5,9)(10,18,24,14,17,15,13,11,25)(12,35,27,30,16,36,22,29,23,19,28,34,21,26,31,32,20,33);(2,5,6)(10,12,19)(11,16,26)(13,22,32)(14,21,30)(15,23,33)(17,28,35)(18,20,29)(24,31,36)(25,27,34)Polycyclic presentation:
2,3^5|b^3=f,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 | #92163⋊C2, C2×#92164, C3×#92164, … |
| maximal normal subgroup of | #92163⋊C2, C2×#92164, C3×#92164, … |
| maximal quotient of | #11757287, C2×#92164, #13090448, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(486, 9);