Finite Group Databasebeta

?

← Prev (#45719624) Next (#45719626) →

C₁₃₁×#33741 #45719625

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

484 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 203 points:

(1,2)(3,6)(4,5)(7,8)(9,10,15,20)(11,16,22,35)(12,25,29,54)(13,30,32,58)(14,33,31,19)(17,38,40,27)(18,41,42,26)(21,43,45,65)(23,50,48,71)(24,51,49,37)(28,57,56,53)(34,59,60,46)(36,63,62,44)(39,55,52,64)(47,70,69,67)(61,68,66,72)(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);(2,5)(6,8)(9,11,15,22)(10,16,20,35)(12,21,29,45)(13,23,32,48)(14,24,31,49)(17,34,40,60)(18,36,42,62)(19,37,33,51)(25,43,54,65)(26,44,41,63)(27,46,38,59)(28,47,56,69)(30,50,58,71)(39,61,52,66)(53,67,57,70)(55,68,64,72);(9,12,26,55,14,28,32,38,15,29,41,64,31,56,13,27)(10,17,30,53,19,39,42,54,20,40,58,57,33,52,18,25)(11,21,44,68,24,47,48,59,22,45,63,72,49,69,23,46)(16,34,50,67,37,61,62,65,35,60,71,70,51,66,36,43);(1,3,4,7)(2,6,5,8)(11,22)(16,35)(21,45)(23,48)(24,49)(34,60)(36,62)(37,51)(43,65)(44,63)(46,59)(47,69)(50,71)(61,66)(67,70)(68,72)

Conjugacy classes & character table

6812 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33536, 26729);