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C₂×#50074 #7705298

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

Aliases

Subgroups

6594 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4,7,9)(5,10,6,8)(11,12)(13,17)(14,18)(15,16);(3,5,7,6)(4,8,9,10)(11,13)(12,14)(15,18)(16,17)(20,23)(21,25);(5,6)(8,10)(12,16)(13,18)(19,20,22,23)(21,24,25,26);(3,6,7,5)(4,8,9,10)(11,13)(12,17)(14,16)(15,18)(19,20)(21,24)(22,23)(25,26);(3,4)(5,10)(6,8)(7,9)(11,14,15,17)(12,13,16,18)(19,21)(20,24)(22,25)(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, 7612494);