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C₂×#52299 #7633638

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

Aliases

Subgroups

7380 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7540834);