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C₂²×#1385 #492870

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

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, 400066);