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C₁₅₁⋊C₃ #90676

• metacyclic
• supersolvable
• metabelian
• solvable
• monolithic
• monomial
• stem
• Frobenius

Aliases

Splittings

Subgroups

4 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 151 points:

(2,3,5)(4,7,12)(6,10,9)(8,14,22)(11,17,19)(13,20,16)(15,24,35)(18,27,32)(21,30,29)(23,33,26)(25,37,51)(28,40,48)(31,43,45)(34,46,42)(36,49,39)(38,53,70)(41,56,67)(44,59,64)(47,62,61)(50,65,58)(52,68,55)(54,72,91)(57,73,88)(60,77,85)(63,80,82)(66,83,79)(69,86,76)(71,89,74)(75,94,109)(78,96,106)(81,98,103)(84,101,100)(87,104,97)(90,107,95)(92,110,93)(99,114,121)(102,116,118)(105,119,115)(108,122,113)(111,124,112)(117,128,132)(120,130,129)(123,133,127)(125,135,126)(131,139,140)(134,141,138)(136,143,137)(142,147,146)(144,148,145)(149,151,150);(1,2,4,8,15,25,38,54,73,37,52,69,87,105,120,131,135,107,68,35,48,64,82,100,115,127,137,139,116,80,43,17,3,6,11,18,28,41,57,75,94,53,71,90,108,123,134,142,143,122,86,49,22,32,45,61,79,97,113,126,128,98,59,27,7,13,21,31,44,60,78,91,109,72,92,111,125,136,144,149,148,133,104,65,33,12,19,29,42,58,76,95,112,114,77,40,14,23,34,47,63,81,99,110,70,88,106,121,132,140,146,150,151,141,119,83,46,20,5,9,16,26,39,55,74,93,96,56,24,36,50,66,84,102,117,124,89,51,67,85,103,118,129,138,145,147,130,101,62,30,10)

Polycyclic presentation:

3,151|b^a=b^32

Conjugacy classes & character table

53 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(453, 1);