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C₂×#24428 #6437816

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

Aliases

Subgroups

5678 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6345012);