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C₇₉×SD₂₅₆ #34119241

• nilpotent
• metacyclic
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

44 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 207 points:

(1,2,8,15)(3,9,21,39)(4,22,26,75)(5,27,30,86)(6,31,33,90)(7,34,32,14)(10,40,44,16)(11,45,48,17)(12,49,52,23)(13,53,55,28)(18,50,67,114)(19,54,70,116)(20,56,69,38)(24,78,81,127)(25,82,80,74)(29,87,76,85)(35,93,96,58)(36,97,99,57)(37,100,101,65)(41,103,105,64)(42,106,107,68)(43,60,91,71)(46,110,111,79)(47,63,92,83)(51,77,84,88)(59,89,102,128)(61,73,108,126)(62,72,109,125)(66,115,118,113)(94,123,104,122)(95,120,117,121)(98,119,112,124)(129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207);(2,9)(3,16)(4,17)(5,23)(6,28)(7,32)(10,11)(12,50)(13,54)(14,56)(15,39)(18,64)(19,68)(20,71)(21,40)(22,35)(24,79)(25,83)(26,45)(27,36)(29,88)(30,49)(31,37)(33,53)(34,38)(41,73)(42,72)(43,92)(44,48)(46,89)(47,91)(51,115)(52,114)(55,116)(57,58)(59,65)(60,69)(61,62)(63,80)(66,123)(67,103)(70,106)(74,117)(75,96)(76,77)(78,94)(81,110)(82,95)(84,113)(85,112)(86,99)(87,98)(90,101)(93,97)(100,102)(104,127)(105,126)(107,125)(108,109)(111,128)(118,122)(119,121)(120,124)

Conjugacy classes & character table

5293 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 540);