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C₂×#43512 #7667750

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

Aliases

Subgroups

6566 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7574946);