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C₂²×#1392 #492892

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

Aliases

Subgroups

2366 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 400088);