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C₈₉×#60462 #36438310

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

2666 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 125 points:

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

Conjugacy classes & character table

5162 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 53450);