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C₂×#20688 #6370866

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

Aliases

Subgroups

5250 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

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

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, 6278062);