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C₂²×#2166 #7622559

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

Aliases

Subgroups

1550 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7529755);