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C₂×#51187 #7706792

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

Aliases

Subgroups

6178 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7613988);