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C₂×#51809 #7707783

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

Aliases

Subgroups

6652 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)(11,12)(13,17)(14,18)(15,16)(19,20,23,24)(21,25,26,22);(4,5)(8,9)(11,13)(12,14)(15,18)(16,17)(20,24)(22,25);(12,16)(13,18)(19,21)(20,22)(23,26)(24,25);(3,5,7,4)(6,9,10,8)(11,13)(12,17)(14,16)(15,18)(19,22)(20,21)(23,25)(24,26);(3,6)(4,8)(5,9)(7,10)(11,14,15,17)(12,13,16,18)(19,21)(20,22)(23,26)(24,25)

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, 7614979);