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C₂×#10948 #354037

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

Aliases

Subgroups

3458 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 261233);