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C₁₂₇×#13336 #44577009

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

586 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 163 points:

(5,6)(7,18)(8,12)(9,25)(10,28)(11,17)(13,20)(14,22)(15,26)(16,24)(19,31)(21,30)(23,32)(27,35)(29,34)(33,36)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163);(1,2)(3,4)(6,12)(7,19)(8,22)(9,26)(10,24)(13,31)(14,16)(15,28)(17,25)(18,35)(20,36)(21,29)(30,32)(33,34);(2,4)(5,7)(6,13)(8,23)(9,27)(10,29)(11,21)(12,30)(14,31)(15,34)(16,35)(17,33)(18,25)(19,24)(20,26)(22,36)(28,32)

Conjugacy classes & character table

5080 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32512, 6324);