Finite Group DatabasebetaFinite Group Databasebeta| order | 34263 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9×C47 · Schur multiplier (H2) = C3 |
| direct product | C47×#10624526 |
| subgroup | G/H | |
|---|---|---|
| center | C9×C47 | #732 |
| commutator | C3×C9 | C3×C9×C47 |
| Frattini, cosocle | C32×C9 | C32×C47 |
| socle | C3×C47 | H(3,𝔽3)⋊C9 |
| prime radical | C47×#6908 | C3 |
| LCS | G ▷ C3×C9 ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C9×C47 ◁ C3×C9×C47 ◁ C32×C9×C47 ◁ G | |
112 conjugacy classes of subgroups.
| minimal degree | μ(G) = 128 |
| transitive degree | μt(G) = 3807 |
A minimal faithful permutation representation — 2 generators on 128 points:
(1,2,7,5,10,27,22,9,33,6,12,28,23,35,58,53,36,65,24,11,38,21,37,57,4,19,26)(3,13,40,16,8,29,15,31,25,18,34,55,48,32,60,49,64,56,17,51,74,50,39,68,20,42,67)(14,43,59,45,41,54,47,30,61,46,62,77,72,66,79,73,63,81,52,76,80,71,75,78,44,69,70)(82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128);(1,3,14)(2,8,30)(4,20,44)(5,16,45)(6,18,46)(7,25,54)(9,34,66)(10,31,62)(11,39,69)(12,32,63)(13,41,19)(15,47,22)(17,52,24)(21,50,71)(23,48,72)(26,29,59)(27,55,61)(28,56,79)(33,60,77)(35,64,76)(36,51,75)(37,42,43)(38,67,78)(40,70,57)(49,73,53)(58,74,81)(65,68,80)4935 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34263, 86);