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C₂×#62040 #10578834

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

Aliases

Subgroups

7104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

98 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10486030);