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C₂²×#1378 #492849

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

Aliases

Subgroups

1698 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400045);