Finite Group Databasebeta

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C₁₃₉×#33465 #48028061

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

642 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

8896 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35584, 26453);