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C₂×#21228 #6371990

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

Aliases

Subgroups

5410 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

(1,2);(4,6)(7,8,9,10)(11,12)(13,22)(14,18)(15,20)(16,25)(17,21)(19,24)(23,26);(3,4,5,6)(8,10)(11,13,16,14,17,24,15,23)(12,18,20,22,21,26,25,19);(11,14,16,24,17,23,15,13)(12,19,20,18,21,22,25,26);(11,15,17,16)(12,20,21,25)(13,23,24,14)(18,22,26,19)

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, 6279186);