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C₂×#51637 #7707549

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

Aliases

Subgroups

7400 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7614745);