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D₇×D₂₅₁⋊C₅ #47975753

• 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 258 points:

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

Conjugacy classes & character table

175 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35140, 14);