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C₂²×#1905 #6371523

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

Aliases

Subgroups

6094 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6278719);