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C₂×#42035 #7640364

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

Aliases

Subgroups

6502 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7547560);