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C₂×#9654 #204174

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

Aliases

Subgroups

1810 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 111370);