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) = C33 |
| direct product | C2×#6855 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C2×C33 | C32 |
| commutator | C3 | C2×C92 |
| Frattini, cosocle | C33 | C2×C32 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C2×C33 ◁ G | |
138 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 486 |
A minimal faithful permutation representation — 2 generators on 29 points:
(1,2)(13,15,18)(16,20,19)(21,22,24,23,25,27,26,28,29);(3,4,6,5,7,9,8,10,11)(12,13,16)(14,15,19)(17,18,20)198 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(486, 62);