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C₂×#23887 #6437597

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

Aliases

Subgroups

6005 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)(9,16)(10,12)(11,15)(13,17)(14,20)(18,21)(19,22);(8,12)(10,20)(13,16)(14,15)(17,18)(21,22);(4,6)(7,8)(9,13)(10,14)(11,15)(12,20)(16,17)(18,22)(19,21);(7,9,11,19)(8,13,15,21)(10,18,20,17)(12,16,14,22)

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, 6344793);