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C₁₀₉×#18298 #42136292

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1024 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 141 points:

(2,9)(3,14)(4,19)(5,15)(10,28)(11,30)(12,21)(13,27)(16,20)(17,18)(22,23)(24,32)(25,26)(29,31)(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);(1,2)(3,10)(4,11)(5,21)(6,24)(7,12)(8,13)(9,15)(14,30)(16,31)(17,26)(18,29)(19,25)(20,28)(22,27)(23,32);(1,3,8,18)(2,10,13,29)(4,15,19,22)(5,20,23,16)(6,14,7,17)(9,25,27,11)(12,26,24,30)(21,28,32,31);(1,4,7,16)(2,11,12,31)(3,15,17,5)(6,20,8,19)(9,26,21,10)(13,25,24,28)(14,23,18,22)(27,30,32,29)

Conjugacy classes & character table

4360 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27904, 11286);