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C₂×#56703 #8099421

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

Aliases

Subgroups

6586 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)(12,16)(14,18)(19,20,23,25)(21,22,26,24);(3,5,7,10)(4,8,6,9)(11,12,15,16)(13,18,17,14)(19,21)(20,24)(22,25)(23,26);(4,6)(8,9)(12,16)(13,17)(19,22,23,24)(20,21,25,26);(3,6,7,4)(5,9,10,8)(11,13,15,17)(12,14,16,18)(19,22)(20,21)(23,24)(25,26);(3,5)(4,8)(6,9)(7,10)(11,14)(12,17)(13,16)(15,18)(19,20)(21,22)(23,25)(24,26)

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 8006617);