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C₂×#21775 #6374180

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

Aliases

Subgroups

4646 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6281376);