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C₂×#23890 #6437598

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

Aliases

Subgroups

6177 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 22 points:

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

Conjugacy classes & character table

86 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6344794);