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C₂×#15737 #609382

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

Aliases

Subgroups

4542 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 516578);