Finite Group DatabasebetaFinite Group Databasebeta| order | 486 |
| isoclinism | isoclinic class of #92301 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C34 |
No aliases for this group.
| Fitting, Sylow | C32⋊H(3,𝔽3) ⋊ C2 |
| derived | C34 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C34 | C2×C3 |
| Frattini, socle | C32 | C3×C3⋊D3 |
| Fitting | C32⋊H(3,𝔽3) | C2 |
| LCS | G ▷ C34 | |
| UCS | C1 | |
258 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 27 |
A minimal faithful permutation representation — 3 generators on 18 points:
(2,7,9,4,5,8)(3,6)(11,16,18,13,14,17)(12,15);(10,11,13)(12,14,17)(15,18,16);(1,2,4)(3,5,8)(6,9,7)Polycyclic presentation:
2,3^5|c^a=c^2,d^a=d^2,e^a=e^2,f^a=f^2,c^b=ce,d^b=df30 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(486, 146);