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C₂×#41234 #7638782

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

Aliases

Subgroups

7508 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7545978);