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C₂×#16422 #610933

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

Aliases

Subgroups

4090 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 518129);