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C₂×#60316 #10574476

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

Aliases

Subgroups

6738 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)(11,12,16,14,15,18,24,23)(13,19,22,26,20,17,25,21);(3,5)(4,7)(6,10)(8,9)(11,13)(12,17)(14,21)(15,20)(16,22)(18,19)(23,26)(24,25);(5,10)(7,9);(4,8)(7,9)(13,20)(17,19)(21,26)(22,25);(11,14,16,18,15,23,24,12)(13,21,22,19,20,26,25,17)

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, 10481672);