Finite Group Databasebeta

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C₁₂₇×#18660 #44582333

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

908 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 159 points:

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

Conjugacy classes & character table

5842 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32512, 11648);