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C₂×#25900 #6446739

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

Aliases

Subgroups

4716 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

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

Conjugacy classes & character table

86 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6353935);