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C₂²×#1976 #6372020

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

Aliases

Subgroups

5090 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 36 points:

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

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, 6279216);