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C₂×#40164 #7637728

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

Aliases

Subgroups

8108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7544924);