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C₂×#34863 #7628029

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

Aliases

Subgroups

6792 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7535225);