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C₂×#36168 #7629804

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

Aliases

Subgroups

7670 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7537000);