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C₂×#61337 #10576491

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

Aliases

Subgroups

6748 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 10483687);