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C₄₇×#491 #15688746

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 71 points:

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

Conjugacy classes & character table

752 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3008, 172);