Finite Group DatabasebetaFinite Group Databasebeta| order | 32340 |
| nilpotency class | 1 |
| automorphism | ? |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C7 |
| abelian | C3×C4×C5×C72×C11 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C2×C3×C5×C72×C11 |
| socle, prime radical | C2×C3×C5×C72×C11 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
240 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 32340 |
A minimal faithful permutation representation — 2 generators on 37 points:
(1,2,3,4)(5,6,7)(8,9,10,11,12)(13,14,15,16,17,18,19)(27,28,29,30,31,32,33,34,35,36,37);(20,21,22,23,24,25,26)32340 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32340, 139);