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C₂×#14567 #521028

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

Aliases

Subgroups

7062 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 428224);