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C₂²×#2115 #7622432

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

Aliases

Subgroups

4066 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7529628);