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C₂²×#1384 #492868

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

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, 400064);