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C₂×#13878 #514059

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

Aliases

Subgroups

7938 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 421255);