Finite Group Databasebeta

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C₁₃₇×#33857 #46883243

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

646 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2,8,14)(3,15,20,50)(4,21,25,46)(5,26,31,44)(6,13,7,12)(9,34,38,18)(10,32,41,24)(11,29,45,30)(16,36,22,59)(17,35,56,39)(19,57,33,42)(23,60,61,40)(27,47,51,37)(28,43,62,64)(48,54,63,53)(49,55,58,52)(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)(4,22)(5,27)(6,19)(7,33)(8,20)(10,39)(11,42)(12,37)(13,47)(14,38)(15,26)(16,25)(17,23)(18,30)(21,58)(24,54)(28,55)(29,34)(31,51)(32,53)(35,41)(36,40)(43,63)(44,50)(45,57)(46,49)(48,64)(52,62)(56,61)(59,60);(1,4)(2,10)(3,16)(5,23)(6,32)(7,24)(8,25)(9,35)(11,40)(12,46)(13,21)(14,41)(15,48)(17,51)(18,52)(19,54)(20,22)(26,43)(27,56)(28,30)(29,62)(31,61)(33,53)(34,55)(36,57)(37,58)(38,39)(42,59)(44,64)(45,60)(47,49)(50,63);(1,4)(2,10)(3,17)(5,28)(6,24)(7,32)(8,25)(9,36)(11,43)(12,21)(13,46)(14,41)(15,49)(16,51)(18,53)(19,55)(20,56)(22,27)(23,30)(26,40)(29,61)(31,62)(33,52)(34,54)(35,57)(37,63)(38,59)(39,42)(44,60)(45,64)(47,48)(50,58)

Conjugacy classes & character table

5891 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35072, 26845);