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C₂×#10784 #353464

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

Aliases

Subgroups

4098 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 22 points:

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 260660);