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C₂×#46871 #7700659

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

Aliases

Subgroups

7198 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7607855);