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C₂×#36726 #7633972

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

Aliases

Subgroups

6774 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7541168);