Finite Group Databasebeta

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C₄₇×#479 #15688734

• 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)(48,49,51,53)(50,54,55,52)(56,57,59,61)(58,64,65,71)(60,68,67,63)(62,69,70,66);(48,50,51,55)(49,52,53,54)(57,61)(62,70)(63,68)(64,71);(56,58,59,65)(57,62,61,70)(60,69,67,66)(63,71,68,64)

Conjugacy classes & character table

893 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3008, 160);