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C₂×#15009 #608061

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

Aliases

Subgroups

4322 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 515257);