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C₂²×#1386 #492872

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

Aliases

Subgroups

1850 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 24 points:

(1,2);(3,4);(5,6,7,8)(9,10,13,17)(11,12,19,21)(14,16,22,24)(15,23,20,18);(9,11,14,18,15,16,21,17,13,19,22,23,20,24,12,10)

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, 400068);