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C₂²×#2192 #7622840

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

Aliases

Subgroups

4042 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530036);