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C₂×#61543 #10576889

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

Aliases

Subgroups

6856 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10484085);