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C₂×#35373 #7628728

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

Aliases

Subgroups

7220 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7535924);