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C₂×#50599 #7705988

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

Aliases

Subgroups

6122 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7613184);