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C₂×#34921 #7628088

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

Aliases

Subgroups

6824 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7535284);