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C₂²×#1388 #492878

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

Aliases

Subgroups

1618 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 36 points:

(1,2);(3,4);(5,6,9,15,12,17,11,28)(7,18,20,30,23,32,22,36)(8,24,26,33,27,16,10,14)(13,21,29,25,31,35,34,19);(5,7,10,21,11,22,27,19,12,23,26,35,9,20,8,25)(6,13,16,30,15,29,14,32,17,31,24,36,28,34,33,18)

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, 400074);