Finite Group DatabasebetaFinite Group Databasebeta| order | 32340 |
| nilpotency class | 1 |
| automorphism | ? |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C22×C3×C5×C11×C49 |
| multiplicative | (ℤ/32897)ˣ, (ℤ/33833)ˣ, (ℤ/41503)ˣ, (ℤ/65794)ˣ, (ℤ/67666)ˣ, (ℤ/83006)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C7 | C22×C3×C5×C7×C11 |
| socle, prime radical | C22×C3×C5×C7×C11 | C7 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
120 conjugacy classes of subgroups.
| minimal degree | μ(G) = 72 |
| transitive degree | μt(G) = 32340 |
A minimal faithful permutation representation — 2 generators on 72 points:
(1,2)(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)(62,63,64,65,66,67,68,69,70,71,72);(3,4)32340 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32340, 37);