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C₂×#8049 #181618

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

Aliases

Subgroups

3086 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 26 points:

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

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, 88814);