Finite Group Databasebeta

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C₁₄₉×#8255 #49187204

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

470 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 173 points:

(2,6)(3,4)(7,8)(9,10,14,18,15,20,13,19)(11,21,22,16,23,12,17,24)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173);(1,2,4,7,5,8,3,6)(9,11,13,17,15,23,14,22)(10,16,19,21,20,24,18,12);(9,12,14,24,15,21,13,16)(10,17,18,11,20,22,19,23)

Conjugacy classes & character table

9536 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38144, 1243);