Finite Group DatabasebetaFinite Group Databasebeta| order | 38637 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C53 · Schur multiplier (H2) = C33×C9 |
| direct product | C53×#10624839 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C3×C53 | C3×#732 |
| commutator, Frattini, cosocle | C3×C9 | C33×C53 |
| LCS | G ▷ C3×C9 ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C53 ◁ C33×C53 ◁ C32×C9×C53 ◁ G | |
222 conjugacy classes of subgroups.
| minimal degree | μ(G) = 134 |
| transitive degree | μt(G) = 4293 |
A minimal faithful permutation representation — 3 generators on 134 points:
(1,2,6)(3,11,31)(4,16,21)(5,10,22)(7,23,42)(8,27,18)(9,30,19)(12,36,67)(13,33,54)(14,41,20)(15,35,63)(17,45,51)(24,56,72)(25,53,73)(26,55,74)(28,61,75)(29,60,47)(32,48,71)(34,50,43)(37,68,78)(38,57,62)(39,69,52)(40,66,49)(44,59,46)(58,79,70)(64,76,80)(65,77,81)(82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134);(1,3,12,5,15,37,19,13,39)(2,7,24,9,25,58,10,26,57)(4,14,38,18,43,70,47,40,72)(6,20,48)(8,11,32,16,33,65,29,35,64)(17,42,71,46,74,80,75,73,81)(21,23,52)(22,50,76)(27,55,67)(28,34,36,44,41,69,45,66,68)(30,49,77)(31,62,59)(51,54,56)(53,78,60)(61,63,79);(3,13,15)(7,25,26)(11,33,35)(12,37,39)(14,40,43)(20,49,50)(23,53,55)(24,57,58)(31,54,63)(32,64,65)(34,41,66)(36,68,69)(38,70,72)(42,73,74)(48,76,77)(52,67,78)(56,62,79)(71,80,81)3021 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38637, 399);