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C₂×#61177 #10576305

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

Aliases

Subgroups

7818 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 10483501);