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C₂×#21224 #6371986

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

Aliases

Subgroups

5538 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)(13,23)(14,26)(15,20)(16,21)(17,22)(18,24)(19,25);(3,4,5,6)(8,10)(11,13,15,24,17,25,16,14)(12,18,21,23,22,26,20,19);(11,14,16,25,17,24,15,13)(12,19,20,26,22,23,21,18);(11,15,17,16)(12,20,22,21)(13,24,25,14)(18,19,26,23)

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6279182);