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C₂×#52345 #8092052

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

Aliases

Subgroups

7882 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)(19,20)(21,25)(22,24)(23,26);(3,4)(5,8)(6,7)(9,10)(11,13)(12,15)(14,16)(17,18)(19,20,22,24)(21,25,26,23);(4,7)(8,10)(12,17)(13,14)(19,20)(21,23)(22,24)(25,26);(3,4)(5,8)(6,7)(9,10)(11,14,16,13)(12,15,17,18)(19,21,22,26)(20,23,24,25);(3,5)(4,8)(6,9)(7,10)(11,15)(12,13)(14,17)(16,18)

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7999248);