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C₂×#34874 #7628040

• 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)(5,8)(6,7)(9,10)(11,12,15,18)(13,16,14,17);(4,7)(8,10)(11,13,15,14)(12,16,18,17)(19,20)(21,25)(22,24)(23,26);(11,13,15,14)(12,17,18,16)(19,21,22,26)(20,23,24,25);(11,14,15,13)(12,17,18,16)(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, 7535236);