Finite Group DatabasebetaFinite Group Databasebeta| order | 34263 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9×C47 · Schur multiplier (H2) = C33 |
| direct product | C47×#10624694 |
| subgroup | G/H | |
|---|---|---|
| center | C9×C47 | C3×H(3,𝔽3) |
| commutator | C32 | C32×C9×C47 |
| Frattini, cosocle | C3×C9 | C33×C47 |
| socle | C3×C47 | C3×C32⋊C9 |
| prime radical | C3×H(3,𝔽3)×C47 | C9 |
| LCS | G ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C9×C47 ◁ C32×C9×C47 ◁ G | |
312 conjugacy classes of subgroups.
| minimal degree | μ(G) = 128 |
| transitive degree | μt(G) = 3807 |
A minimal faithful permutation representation — 3 generators on 128 points:
(1,2,6,4,9,21,16,28,45,5,10,20,17,29,44,39,54,67,18,8,26,40,27,52,63,53,73)(3,11,19,14,31,43,37,56,66,15,7,22,38,24,47,62,50,69,13,25,42,36,51,65,61,72,79)(12,32,41,34,57,64,59,75,78,33,30,46,58,55,68,76,74,80,35,23,48,60,49,70,77,71,81)(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);(1,3,12)(2,7,23)(4,14,34)(5,15,33)(6,19,41)(8,11,30)(9,24,49)(10,25,32)(13,35,18)(16,37,59)(17,38,58)(20,22,46)(21,43,64)(26,42,48)(27,31,55)(28,50,71)(29,51,57)(36,60,40)(39,62,76)(44,47,68)(45,66,78)(52,65,70)(53,56,74)(54,72,75)(61,77,63)(67,69,80)(73,79,81);(3,13,15)(7,11,25)(12,33,35)(14,36,38)(19,42,22)(23,32,30)(24,31,51)(34,58,60)(37,61,62)(41,46,48)(43,65,47)(49,57,55)(50,56,72)(59,76,77)(64,68,70)(66,79,69)(71,75,74)(78,80,81)4935 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34263, 254);