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C₈₉×#61051 #36438899

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

2734 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 54039);