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C₂×#23439 #6431782

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

Aliases

Subgroups

7610 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)(9,17)(10,16)(11,14)(12,15)(13,18)(19,21)(20,22);(4,6)(7,9)(8,13)(10,19)(11,18)(12,20)(14,22)(15,21)(16,17);(8,14)(9,18)(10,11)(15,16)(17,22)(19,20);(8,15)(13,21)(14,16)(17,22)

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6338978);