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C₂×#14991 #608040

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

Aliases

Subgroups

4974 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

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

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, 515236);