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C₈₉×#60651 #36438499

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

3138 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 53639);