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C₁₃₉×#33470 #48028066

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

632 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 203 points:

(1,2)(3,14,18,44)(4,20)(5,10)(6,27)(7,13)(8,17,33,52)(9,23)(11,25)(12,26)(15,45,48,64)(16,43,19,38)(21,35)(22,39)(24,36)(28,41,53,32)(29,34)(30,37)(31,57,62,60)(40,50)(42,49,61,46)(47,63,51,54)(55,58)(56,59)(65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203);(1,3)(2,8)(4,15)(5,16)(6,28)(7,18)(9,31)(10,32)(11,38)(12,41)(13,33)(14,37)(17,50)(19,26)(20,54)(21,46)(22,57)(23,49)(24,48)(25,52)(27,44)(29,60)(30,53)(34,45)(35,62)(36,63)(39,64)(40,43)(42,55)(47,56)(51,58)(59,61);(1,4,5,23,7,24,26,21)(2,9,12,20,13,35,10,36)(3,15,16,49,18,48,19,46)(6,29,25,56,30,22,50,58)(8,31,41,54,33,62,32,63)(11,39,27,59,40,34,37,55)(14,42,38,64,44,61,43,45)(17,51,28,60,52,47,53,57);(1,5,7,26)(2,10,13,12)(3,16,18,19)(4,21,24,23)(6,25,30,50)(8,32,33,41)(9,20,35,36)(11,37,40,27)(14,43,44,38)(15,46,48,49)(17,28,52,53)(22,56,29,58)(31,54,62,63)(34,55,39,59)(42,64,61,45)(47,60,51,57)

Conjugacy classes & character table

6394 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35584, 26458);