Finite Group Databasebeta

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C₁₃₇×#33442 #46882828

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

642 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 201 points:

(1,2,6,12,7,11,26,36,8,13,27,37,5,23,25,49)(3,14,17,39,16,9,28,30,18,31,43,55,24,32,50,56)(4,10,21,35,22,34,48,58,19,33,44,57,20,45,47,61)(15,38,42,59,41,29,51,53,40,54,60,64,46,52,62,63)(65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201);(1,3)(2,9)(4,15)(5,24)(6,17)(7,16)(8,18)(10,29)(11,31)(12,30)(13,32)(14,23)(19,40)(20,46)(21,42)(22,41)(25,50)(26,28)(27,43)(33,52)(34,54)(35,53)(36,55)(37,56)(38,45)(39,49)(44,60)(47,62)(48,51)(57,63)(58,64)(59,61);(1,4,6,21,7,22,26,48,8,19,27,44,5,20,25,47)(2,10,12,35,11,34,36,58,13,33,37,57,23,45,49,61)(3,15,17,42,16,41,28,51,18,40,43,60,24,46,50,62)(9,29,30,53,31,54,55,64,32,52,56,63,14,38,39,59);(4,19)(10,33)(15,40)(20,22)(21,44)(29,52)(34,45)(35,57)(38,54)(41,46)(42,60)(47,48)(51,62)(53,63)(58,61)(59,64)

Conjugacy classes & character table

12056 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35072, 26430);