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C₂×#61194 #10576355

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

Aliases

Subgroups

7770 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)(12,17)(13,20)(14,16)(18,25)(21,23)(24,26);(3,5)(4,7)(6,10)(8,9)(11,12,15,17)(13,18,21,24)(14,22,16,19)(20,26,23,25);(11,13)(12,18)(14,20)(15,21)(16,23)(17,24)(19,25)(22,26);(5,10)(7,9)(12,17)(18,24)(19,22)(25,26);(11,14,15,16)(12,19,17,22)(13,20,21,23)(18,25,24,26)

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10483551);