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C₂×#9648 #204049

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

Aliases

Subgroups

2074 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 111245);