Finite Group Databasebeta

?

← Prev (#28425845) Next (#28425847) →

C₅₉×#13737 #28425846

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 187 points:

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

Conjugacy classes & character table

9440 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 6725);