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C₂×#13778 #513382

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

Aliases

Subgroups

7234 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 420578);