Finite Group DatabasebetaFinite Group Databasebeta| order | 32340 |
| automorphism | ? |
| homology | Abelianization (H1) = C49 · Schur multiplier (H2) = C2 |
| direct product | C49×PSL(2,𝔽11) |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C49 | PSL(2,𝔽11) |
| commutator, hypocenter | PSL(2,𝔽11) | C49 |
| Frattini, cosocle | C7 | C7×PSL(2,𝔽11) |
| socle, prime radical | C7×PSL(2,𝔽11) | C7 |
| LCS | G ▷ PSL(2,𝔽11) | |
| UCS | C1 ◁ C49 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 60 |
| transitive degree | μt(G) = 539 |
A minimal faithful permutation representation — 2 generators on 60 points:
(50,57,53,55,56,58)(51,59)(52,60,54);(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)(50,52,55)(51,53,57)(56,58,59)392 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32340, 659);