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C₂²×#2194 #7622841

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

Aliases

Subgroups

3978 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7530037);