Finite Group DatabasebetaFinite Group Databasebeta| order | 34263 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C47 · Schur multiplier (H2) = C35 |
| direct product | C47×#10624731 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C32×C47 | C3×H(3,𝔽3) |
| commutator, Frattini, cosocle | C33 | C33×C47 |
| prime radical | C47×C32⋊H(3,𝔽3) | C3 |
| LCS | G ▷ C33 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C32×C47 ◁ C34×C47 ◁ G | |
560 conjugacy classes of subgroups.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 3807 |
A minimal faithful permutation representation — 3 generators on 83 points:
(1,2,4)(3,6,8)(5,9,7)(10,11,14)(12,18,22)(13,17,23)(15,24,20)(16,27,21)(19,29,32)(25,35,36)(26,34,31)(28,33,30)(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);(10,12,19,13,20,30,21,31,36)(11,15,25,17,26,29,16,18,28)(14,22,32,23,24,33,27,34,35);(2,5,6)(4,8,9)4935 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34263, 291);