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C₂²×#1791 #6370737

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

Aliases

Subgroups

17210 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6277933);