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C₈₉×#61054 #36438902

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

2710 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 54042);