Finite Group DatabasebetaFinite Group Databasebeta| order | 37485 |
| nilpotency class | 1 |
| automorphism | ? |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C7 |
| abelian | C5×C72×C9×C17 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3 | C3×C5×C72×C17 |
| socle, prime radical | C3×C5×C72×C17 | C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
120 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 37485 |
A minimal faithful permutation representation — 2 generators on 45 points:
(1,2,3,4,5,6,7,8,9)(10,11,12,13,14)(15,16,17,18,19,20,21)(29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45);(22,23,24,25,26,27,28)37485 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37485, 5);