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#555×C₇₁ #17985686

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

236 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 87 points:

(1,2)(3,7)(4,8)(5,6)(10,11)(14,15)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87);(2,6)(4,7)(9,10,13,11)(12,15,16,14);(1,3,5,8)(2,7,6,4)(9,11,13,10)(12,15,16,14);(1,4,5,7)(2,8,6,3)(9,12,13,16)(10,14,11,15)

Conjugacy classes & character table

1775 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4544, 236);