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C₂×#23048 #6382003

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

Aliases

Subgroups

2662 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6289199);