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C₂×#28467 #6465617

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

3722 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6372813);