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C₂×#23402 #6431718

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

Aliases

Subgroups

8154 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)(10,14)(11,19)(12,15)(13,17)(18,22)(20,21);(7,9)(8,13)(10,17)(11,20)(12,18)(14,22)(15,21)(16,19);(4,6)(10,11)(13,21)(14,19)(17,20);(7,10,12,11)(8,14,15,19)(9,17,18,20)(13,22,21,16)

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, 6338914);