Finite Group DatabasebetaFinite Group Databasebeta| order | 486 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C92 · Schur multiplier (H2) = C3 |
| direct product | C2×#6864 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C3×C9 | C32 |
| commutator | C3 | C2×C92 |
| Frattini, cosocle | C3×C9 | C2×C32 |
| socle, prime radical | C2×C32 | C3×C9 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C9 ◁ G | |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 38 |
| transitive degree | μt(G) = 486 |
A minimal faithful permutation representation — 2 generators on 38 points:
(1,2)(12,13,16,14,18,24,20,27,32,15,19,23,21,28,31,29,35,37,22,17,25,30,26,33,36,34,38);(3,4,6,5,7,9,8,10,11)(13,17,19)(16,23,25)(18,26,28)(24,31,33)(27,34,35)(32,37,38)198 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(486, 71);