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C₂×#10992 #357528

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

Aliases

Subgroups

5794 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 26 points:

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

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, 264724);