Finite Group DatabasebetaFinite Group Databasebeta| order | 486 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #6878 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3×C9 |
| direct product | C2×#6879 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C3 | #732 |
| commutator, Frattini, cosocle | C3×C9 | C2×C32 |
| LCS | G ▷ C3×C9 ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C2×C3 ◁ C2×C32 ◁ C2×C3×C9 ◁ G | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 54 |
A minimal faithful permutation representation — 2 generators on 29 points:
(1,2)(3,4,7)(5,9,14)(6,10,17)(8,18,23)(11,21,25)(12,19,15)(13,22,16)(20,27,29)(24,28,26);(4,8,19,10,20,28,22,21,9)(7,14,25,16,26,27,17,15,18)70 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(486, 86);