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C₂²×#2161 #7622539

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

Aliases

Subgroups

1922 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7529735);