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C₂×#25500 #6452050

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

Aliases

Subgroups

3976 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6359246);