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C₂×#35687 #7629620

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

Aliases

Subgroups

22678 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7536816);