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C₂×#35871 #7629268

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

Aliases

Subgroups

5958 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7536464);