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C₈₉×#61197 #36439045

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

2046 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 129 points:

(1,2,4,6)(3,7,8,5)(9,10)(11,16)(12,25)(13,18)(14,19)(15,20)(17,26)(21,35)(22,30)(23,34)(24,31)(27,32)(28,33)(29,36)(37,40)(38,39)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129);(1,3)(2,5)(4,8)(6,7)(9,11,15,24)(10,16,20,31)(12,21,27,38)(13,22,14,23)(17,29,33,40)(18,30,19,34)(25,35,32,39)(26,36,28,37);(9,12)(10,17)(11,21)(13,26)(14,28)(15,27)(16,29)(18,32)(19,25)(20,33)(22,36)(23,37)(24,38)(30,39)(31,40)(34,35);(3,8)(5,7)(9,13,15,14)(10,18,20,19)(11,22,24,23)(12,26,27,28)(16,30,31,34)(17,32,33,25)(21,36,38,37)(29,39,40,35);(9,13,15,14)(10,19,20,18)(11,23,24,22)(12,26,27,28)(16,30,31,34)(17,25,33,32)(21,37,38,36)(29,39,40,35)

Conjugacy classes & character table

4895 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 54185);