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C₂×#48059 #7703154

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

Aliases

Subgroups

6272 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7610350);