Finite Group Databasebeta

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C₁₁×#15691107 #46805486

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

242 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 161 points:

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

Conjugacy classes & character table

2695 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34375, 50);