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C₈₉×#61614 #36439462

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

2120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 113 points:

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

Conjugacy classes & character table

4361 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 54602);