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C₂×#35849 #7629213

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

Aliases

Subgroups

6032 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7536409);