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C₂×#48910 #7704857

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

Aliases

Subgroups

6744 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7612053);