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C₂×#32977 #6629118

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

Aliases

Subgroups

4652 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

98 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6536314);