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C₂²×#2822 #7633395

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

Aliases

Subgroups

7370 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 32 points:

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7540591);