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C₁₉×#13737 #18019696

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 147 points:

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

Conjugacy classes & character table

3040 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 6725);