Finite Group DatabasebetaFinite Group Databasebeta| order | 31746 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊#15668368 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C13×C37 | C2×C3 |
| LCS | G ▷ C11×C13×C37 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 61 |
| transitive degree | μt(G) = 5291 |
A minimal faithful permutation representation — 2 generators on 61 points:
(2,3)(4,5)(6,7)(8,9)(10,11)(13,17,18,14,15,19)(16,23,22,20,21,24)(26,30,31,27,28,32)(29,38,39,33,34,48)(35,51,43,41,42,53)(36,50,46,44,40,37)(45,61,58,55,52,59)(47,49,54,56,57,60);(1,2,4,6,8,10,11,9,7,5,3)(12,13,16,15,19,22,21,23,24,18,17,20,14)(25,26,29,35,43,54,61,51,55,44,28,32,37,47,58,39,50,38,49,57,34,40,48,59,56,46,31,30,36,45,42,52,60,53,41,33,27)Polycyclic presentation:
2,3,11,13,37|c^a=c^10,d^a=d^12,e^a=e^36,d^b=d^3,e^b=e^10901 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31746, 48);