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C₂×#50641 #7706449

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

Aliases

Subgroups

8102 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7613645);