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C₂×#23910 #6437433

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

Aliases

Subgroups

6810 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6344629);