Finite Group DatabasebetaFinite Group Databasebeta| order | 36540 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C2 |
| direct product | C3×PSL(2,𝔽29) |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C3 | PSL(2,𝔽29) |
| commutator, hypocenter | PSL(2,𝔽29) | C3 |
| Frattini | C1 | G |
| LCS | G ▷ PSL(2,𝔽29) | |
| UCS | C1 ◁ C3 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 90 |
A minimal faithful permutation representation — 2 generators on 33 points:
(4,25,17,27,24,12,7,30,14,6,13,15,19,33,32)(5,10,11,31,26,9,18,16,28,8,20,21,22,29,23);(1,2,3)(4,18,9,11,26,23,14)(5,6,24,7,27,17,28)(8,12,20,19,29,16,30)(10,25,13,21,33,31,32)51 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36540, 541);