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C₂×#16544 #611098

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

Aliases

Subgroups

5454 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 518294);