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C₂×#7904 #180981

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

Aliases

Subgroups

2506 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 22 points:

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 88177);