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C₂×C₈₉×#3529 #36440539

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

7418 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 115 points:

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

Conjugacy classes & character table

6764 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 55679);