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C₂×#44776 #7669146

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

Aliases

Subgroups

8488 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 22 points:

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

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, 7576342);