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C₂×#21491 #6372750

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

Aliases

Subgroups

3314 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)(11,12,15,19,16,14,18,23)(13,17,22,25,20,21,24,26);(3,4,5,6)(11,13)(12,17)(14,21)(15,22)(16,20)(18,24)(19,25)(23,26);(8,10)(13,20)(17,21)(22,24)(25,26);(11,14,15,23,16,12,18,19)(13,21,22,26,20,17,24,25)

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, 6279946);