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C₂×#48117 #7703298

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

Aliases

Subgroups

5952 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7610494);