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C₂×#35379 #7628735

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

Aliases

Subgroups

6268 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7535931);