Finite Group Databasebeta

?

← Prev (#46883236) Next (#46883238) →

C₁₃₇×#33851 #46883237

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

674 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

7535 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35072, 26839);