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C₂×#13347 #498920

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

Aliases

Subgroups

2542 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

62 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 406116);