Finite Group DatabasebetaFinite Group Databasebeta| order | 17325 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | ? |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C3 |
| abelian | C32×C7×C11×C25 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C5 | C32×C5×C7×C11 |
| socle, prime radical | C32×C5×C7×C11 | C5 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
72 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 17325 |
A minimal faithful permutation representation — 2 generators on 49 points:
(1,2,3)(7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31)(32,33,34,35,36,37,38)(39,40,41,42,43,44,45,46,47,48,49);(4,5,6)17325 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17325, 5);