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C₂×#14343 #515251

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

Aliases

Subgroups

6106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 422447);