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C₂×#13331 #498856

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

Aliases

Subgroups

1900 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)(9,18)(10,14)(11,16)(12,13)(15,20)(17,21)(19,22);(4,6)(7,9)(8,13)(10,21)(11,19)(12,20)(14,18)(15,22);(8,14)(9,19)(10,20)(11,21)(13,22)(15,17)(16,18)

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 406052);