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C₁₂₇×#13618 #44577291

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

290 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 195 points:

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

Conjugacy classes & character table

6604 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32512, 6606);