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C₂²×#1858 #6371290

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

Aliases

Subgroups

4554 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6278486);