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C₂×#56325 #8098945

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

Aliases

Subgroups

6678 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 8006141);