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C₂×#60236 #10574288

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

Aliases

Subgroups

8192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10481484);