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C₂×#60314 #10574474

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

Aliases

Subgroups

6906 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10481670);