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C₂×#40417 #7638013

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

Aliases

Subgroups

6080 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7545209);