Finite Group Databasebeta

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C₄₇×#341 #15688596

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 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)(48,49)(50,51)(52,53,55,60,57,61,56,59)(54,62,63,58,65,66,64,67);(49,51)(52,54,56,64,57,65,55,63)(53,58,60,66,61,67,59,62)

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, 22);