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C₈₉×#61060 #36438908

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

2686 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)(9,23)(10,13)(11,18)(14,24)(16,31)(17,27)(19,26)(20,34)(21,35)(22,29)(25,33)(28,32)(30,36)(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);(5,7,10,19)(6,11,13,27)(8,20,22,16)(9,17,24,18)(12,28,29,25)(14,26,23,15)(21,33,36,32)(30,31,35,34);(2,4)(5,8,10,22)(6,12,13,29)(7,16,19,20)(9,21,24,36)(11,25,27,28)(14,30,23,35)(15,31,26,34)(17,32,18,33);(7,17)(9,24)(11,26)(14,23)(15,27)(16,32)(18,19)(20,33)(21,36)(25,34)(28,31)(30,35);(6,13)(11,27)(12,29)(14,23)(15,26)(25,28)(30,35)(31,34)

Conjugacy classes & character table

4628 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 54048);