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C₂×#41140 #7638669

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7545865);