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C₂×#29256 #6463590

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

Aliases

Subgroups

2582 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6370786);