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D₇×D₂₇₁⋊C₅ #49182006

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 278 points:

(1,2,4,6,7,5,3)(9,13,14,32,37,10,11,19,21,61)(12,26,27,93,98,16,17,48,50,165)(15,42,43,44,72,23,24,81,83,85)(18,55,56,49,141,29,30,109,95,96)(20,66,67,209,188,34,35,128,130,119)(22,76,77,73,74,39,40,78,38,84)(25,87,88,217,167,45,46,152,154,243)(28,103,104,257,139,52,53,176,178,220)(31,113,114,224,148,58,59,194,195,227)(33,123,124,62,199,63,64,202,120,121)(36,135,47,159,160,69,70,90,91,238)(41,144,65,168,169,79,80,126,99,245)(51,171,172,140,71,100,101,250,75,137)(54,183,112,268,244,106,107,191,192,267)(57,189,190,231,221,110,111,153,249,187)(60,184,198,236,237,116,117,197,158,277)(68,215,216,86,229,132,133,246,150,151)(82,118,105,263,264,147,138,180,181,200)(89,235,204,205,146,156,157,125,259,164)(92,161,241,212,228,162,163,239,242,274)(94,223,233,122,214,143,166,155,131,201)(97,211,207,173,213,149,129,127,251,252)(102,254,255,247,248,174,175,278,170,270)(108,115,240,271,136,185,186,196,276,218)(134,260,261,222,145,210,179,203,142,225)(177,219,269,265,266,226,258,193,182,272)(206,256,253,262,234,208,273,230,275,232);(2,3)(4,5)(6,7)(8,9,12,18,31,60,118,137,69,34,11,15,25,47,92,164,43,84,149,95,17,28,54,108,187,220,85,61,119,56,30,57,112,193,270,271,151,121,200,111,59,115,197,216,245,241,172,201,272,192,117,183,267,243,165,238,252,209,263,265,180,103,177,225,144,224,275,260,176,174,100,48,94,77,76,142,154,215,258,218,135,96,140,73,32,62,122,128,210,132,66,129,212,223,64,125,206,207,126,63,14,22,41,50,99,170,249,274,227,147,24,44,86,101,173,253,88,155,234,190,46,89,158,175,256,278,157,124,203,114,91,161,240,178,259,277,237,205,257,196,163,159,194,261,202,235,255,273,254,236,156,87,153,232,233,152,230,251,171,150,83,42,82,148,228,231,247,168,93,79,39,19,33,65,127,208,204,123,166,242,211,35,68,134,67,131,120,21,38,75,141,70,136,219,133,217,222,40,78,143,27,51,102,104,179,262,195,80,145,226,53,105,182,181,130,213,160,98,167,244,107,184,268,266,214,250,239,169,246,198,186,113,189,264,199,229,276,248,269,191,110,55,109,188,37,72,139,221,185,106,52,26,49,97,74,81,146,162,90,45,23,13,20,36,71,138,116,58,29,16,10)

Conjugacy classes & character table

185 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37940, 14);