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C₂×#22406 #6379008

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

Aliases

Subgroups

5024 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6286204);