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C₂×#17666 #6343787

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

Aliases

Subgroups

4646 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6250983);