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C₂×#35621 #7629024

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

Aliases

Subgroups

11326 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7536220);