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C₂×#45529 #7701922

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

Aliases

Subgroups

8658 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7609118);