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C₂×#12599 #492933

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

Aliases

Subgroups

1670 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400129);