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C₂×#53907 #8102666

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

Aliases

Subgroups

7780 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 8009862);