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C₁₀₉×#11464 #42129458

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

310 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 157 points:

(1,2)(3,9,11,6)(4,7)(5,8)(10,15,16,13)(12,14)(17,18,21,26,22,27,36,44,23,28,37,45,20,25,34,42)(19,29,32,46,31,39,47,43,30,41,35,48,33,24,38,40)(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);(1,3)(2,6)(4,10)(5,11)(7,13)(8,9)(12,16)(14,15)(17,19)(18,24)(20,33)(21,35)(22,31)(23,30)(25,41)(26,43)(27,29)(28,39)(32,37)(34,47)(36,38)(40,45)(42,46)(44,48);(1,4,5,12)(2,7,8,14)(3,10,11,16)(6,13,9,15)(19,30)(24,39)(29,41)(31,33)(32,35)(38,47)(40,43)(46,48)

Conjugacy classes & character table

6976 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27904, 4452);