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C₂×#52296 #7633641

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

Aliases

Subgroups

6346 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7540837);