Finite Group Databasebeta

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C₄₇×#424 #15688679

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

114 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 67 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)(49,51)(52,53,55,58,56,59,62,65)(54,57,61,64,60,63,66,67);(48,49,50,51)(52,54)(53,57)(55,61)(56,60)(58,64)(59,63)(62,66)(65,67);(54,60)(57,63)(61,66)(64,67)

Conjugacy classes & character table

1316 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3008, 105);