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C₂×#24407 #6437993

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

Aliases

Subgroups

4998 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6345189);