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C₂×#17500 #6343007

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

Aliases

Subgroups

4584 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 18 points:

(1,2);(3,4)(5,7)(6,8)(9,10)(11,12,14,17,15,13,18,16);(4,7)(5,10)(8,9)(11,13)(12,15)(14,16)(17,18);(4,8)(7,9)(12,13)(16,17);(4,8)(7,9)

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, 6250203);