Finite Group DatabasebetaFinite Group Databasebeta| order | 32340 |
| automorphism | ? |
| homology | Abelianization (H1) = C11×C49 · Schur multiplier (H2) = C2 |
| direct product | C11×C49×A5 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C11×C49 | A5 |
| commutator, hypocenter | A5 | C11×C49 |
| Frattini, cosocle | C7 | C7×C11×A5 |
| socle, prime radical | C7×C11×A5 | C7 |
| LCS | G ▷ A5 | |
| UCS | C1 ◁ C11×C49 | |
54 conjugacy classes of subgroups.
| minimal degree | μ(G) = 65 |
| transitive degree | μt(G) = 2695 |
A minimal faithful permutation representation — 2 generators on 65 points:
(61,62,63,64,65);(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60)(61,62,63,65,64)2695 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32340, 657);