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C₂×#15221 #608539

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

Aliases

Subgroups

4030 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 515735);