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C₂²×#3344 #10576559

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

Aliases

Subgroups

6866 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 28 points:

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

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, 10483755);