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C₂×#11152 #357912

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

Aliases

Subgroups

2574 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 22 points:

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

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, 265108);