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(C₃⋊D₃)⋊(D₁₃₁⋊C₅) #37556087

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 137 points:

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

Polycyclic presentation:

2^2,5,3^2,131|e^a=e^2,f^a=f^130,d^b=d^2,e^b=e^2,f^c=f^58

Conjugacy classes & character table

123 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23580, 62);