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C₃×#6410 #10620593

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 26 points:

(1,2,3)(4,5,7,9,10,8,6)(11,13,15,21)(12,16,18,19)(14,22,23,20)(17,25,26,24);(5,6)(7,8)(9,10)(11,12,14,17,15,18,23,26)(13,19,20,25,21,16,22,24)

Conjugacy classes & character table

123 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(672, 175);