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C₁₃₁×#29905 #45715789

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

730 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 195 points:

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

Conjugacy classes & character table

4454 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33536, 22893);