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C₂×#34808 #7627973

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

Aliases

Subgroups

6164 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7535169);