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C₂×#14300 #515118

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

Aliases

Subgroups

8010 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 22 points:

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

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, 422314);