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C₂×#35080 #7628272

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

Aliases

Subgroups

7502 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(5,9)(8,10)(11,12)(13,18)(14,15)(16,17)(20,24)(22,25);(4,7)(8,10)(12,17)(13,14)(20,24)(21,26);(3,4)(5,8)(6,7)(9,10)(11,13,16,14)(12,18,17,15)(19,20,23,24)(21,25,26,22);(3,4)(5,8)(6,7)(9,10)(11,14,16,13)(12,15,17,18)(19,21)(20,25)(22,24)(23,26);(3,5)(4,8)(6,9)(7,10)(11,15)(12,13)(14,17)(16,18)(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, 7535468);