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C₇₉×D₁₂₈ #34119240

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

Aliases

Subgroups

46 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 539);