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C₂×#43816 #7668022

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

Aliases

Subgroups

6712 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7575218);