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C₂×#8114 #181376

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

Aliases

Subgroups

3090 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)(13,19,20,16)(14,18)(15,17)(21,25,26,23)(22,24);(3,5)(4,7,8,9)(6,10)(11,13,14,21,15,20,22,26)(12,16,18,23,17,19,24,25);(5,10)(7,9)

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, 88572);