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C₂×#14342 #515250

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

Aliases

Subgroups

7154 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 422446);