Finite Group Databasebeta

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C₁₅₁×#23893 #50328818

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1610 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 215 points:

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

Conjugacy classes & character table

6040 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38656, 16881);