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C₂×#42234 #7640558

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

Aliases

Subgroups

5700 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7547754);