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C₂×#20932 #6371412

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

Aliases

Subgroups

7002 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6278608);