Finite Group DatabasebetaFinite Group Databasebeta| order | 34263 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C47 · Schur multiplier (H2) = C32 |
| direct product | C47×#10624488 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C32×C47 | #732 |
| commutator, Frattini, cosocle | C32×C9 | C32×C47 |
| prime radical | C3×C47×#732 | C3 |
| LCS | G ▷ C32×C9 ▷ C33 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C32×C47 ◁ C33×C47 ◁ C32×C9×C47 ◁ G | |
124 conjugacy classes of subgroups.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 3807 |
A minimal faithful permutation representation — 2 generators on 83 points:
(2,4,6)(10,11,14)(12,19,23)(13,18,24)(15,25,20)(16,29,21)(17,30,22)(26,34,32)(27,35,36)(28,33,31)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83);(1,2,5)(3,6,9)(4,8,7)(11,15,26,18,28,19,17,27,16)(14,23,25,30,34,35,24,29,33)2679 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34263, 48);