Finite Group DatabasebetaFinite Group Databasebeta| order | 486 |
| isoclinism | isoclinic class of (3−1+2⋊C9)⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (3−1+2⋊C9)⋊C2 |
| Fitting, derived, Sylow | 3−1+2⋊C9 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | 3−1+2⋊C9 | C2 |
| Frattini | C33 | C3⋊D3 |
| socle | C32 | #272 |
| LCS | G ▷ 3−1+2⋊C9 | |
| UCS | C1 | |
73 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 81 |
A minimal faithful permutation representation — 3 generators on 18 points:
(2,5)(3,7)(4,9)(6,8)(11,14)(12,13)(15,18)(16,17);(1,8,7,9,2,5,4,3,6)(11,15,16)(14,17,18);(1,3,5,9,8,6,4,2,7)(10,11,14)(12,15,17)(13,16,18)Polycyclic presentation:
2,3^5|b^3=e^2,c^3=e^2,b^a=b^2e,c^a=c^2e,d^a=df^2,e^a=e^2,f^a=f^2,c^b=cd,d^b=df30 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(486, 57);