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C₂×#40007 #7638048

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

Aliases

Subgroups

6688 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7545244);