Finite Group DatabasebetaFinite Group Databasebeta| order | 486 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of C32⋊H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33 · Schur multiplier (H2) = C9 |
| direct product | C2×#6896 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C32 | C33 |
| commutator, Frattini, cosocle | C32 | C2×C33 |
| prime radical | C2×C33 | C32 |
| LCS | G ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C2×C32 ◁ G | |
120 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 162 |
A minimal faithful permutation representation — 3 generators on 20 points:
(1,2)(4,8,10)(5,9,11)(13,16,14)(17,18,19);(3,4,9,7,10,11,6,8,5)(12,13,17,15,16,19,20,14,18);(3,5,8,6,11,10,7,9,4)(12,14,19,15,13,18,20,16,17)102 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(486, 202);