Finite Group Databasebeta

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C₁₃₇×#33837 #46883223

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

680 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 173 points:

(1,2)(3,4)(6,12)(7,11)(8,16)(9,21)(13,29)(14,31)(15,28)(17,24)(18,33)(19,32)(20,26)(22,25)(27,34)(30,35)(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);(5,6,10,15)(7,13,11,25)(8,18,20,31)(9,22,24,29)(12,17,28,21)(14,32,33,19)(16,35,26,27)(23,30,36,34);(2,4)(5,7,10,11)(6,13,15,25)(8,16,20,26)(9,17,24,21)(12,22,28,29)(14,30,33,34)(18,35,31,27)(19,23,32,36);(5,8,10,20)(6,14,15,33)(7,16,11,26)(9,23,24,36)(12,27,28,35)(13,30,25,34)(17,32,21,19)(18,29,31,22)

Conjugacy classes & character table

5891 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35072, 26825);