Finite Group DatabasebetaFinite Group Databasebeta| order | 36540 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C7×C29 · Schur multiplier (H2) = C2 |
| direct product | C3×C7×C29×A5 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C3×C7×C29 | A5 |
| commutator, hypocenter | A5 | C3×C7×C29 |
| Frattini | C1 | G |
| LCS | G ▷ A5 | |
| UCS | C1 ◁ C3×C7×C29 | |
84 conjugacy classes of subgroups.
| minimal degree | μ(G) = 44 |
| transitive degree | μt(G) = 3045 |
A minimal faithful permutation representation — 2 generators on 44 points:
(4,8,7,6,5);(1,2,3)(4,5,7,6,8)(9,10,11,12,13,14,15)(16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44)3045 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36540, 538);