Finite Group DatabasebetaFinite Group Databasebeta| order | 17325 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | ? |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C5 |
| abelian | C52×C7×C9×C11 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3 | C3×C52×C7×C11 |
| socle, prime radical | C3×C52×C7×C11 | C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
96 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 17325 |
A minimal faithful permutation representation — 2 generators on 37 points:
(1,2,3,4,5,6,7,8,9)(10,11,12,13,14)(20,21,22,23,24,25,26)(27,28,29,30,31,32,33,34,35,36,37);(15,16,17,18,19)17325 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17325, 9);