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C₂×#35378 #7628734

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

Aliases

Subgroups

7584 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7535930);