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C₂×#49206 #7704870

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

Aliases

Subgroups

6830 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7612066);