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C₂×#10746 #353429

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

Aliases

Subgroups

4262 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)(9,15,16,12)(10,14)(11,13)(17,21,22,19)(18,20);(7,9,10,17,11,16,18,22)(8,12,14,19,13,15,20,21);(4,6)(7,8)(9,12)(10,14)(11,13)(15,16)(17,19)(18,20)(21,22)

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, 260625);