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#552×C₇₁ #17985683

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

214 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2,5,6)(3,4,7,8)(11,15)(13,16)(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)(4,8)(9,10,12,14)(11,13,15,16);(1,3,5,7)(2,4,6,8)(9,11)(10,13)(12,15)(14,16);(1,4)(2,7)(3,6)(5,8)

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, 233);