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C₂×#14315 #515136

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

Aliases

Subgroups

5026 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 422332);