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C₂×#45359 #7669791

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

Aliases

Subgroups

6130 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)(13,17)(15,18)(19,20,23,24)(21,22,25,26);(4,7)(5,10)(11,12)(13,18)(14,16)(15,17)(20,24)(22,26);(3,4,6,7)(5,8,10,9)(11,12,14,16)(13,15,17,18)(19,21,23,25)(20,22,24,26);(3,4)(5,8)(6,7)(9,10)(11,12)(13,15)(14,16)(17,18)(19,22)(20,25)(21,24)(23,26);(3,5,6,10)(4,8,7,9)(11,13,14,17)(12,15,16,18)

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7576987);