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C₂×#24438 #6437819

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

Aliases

Subgroups

5120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6345015);