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C₂²×#2827 #7633360

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

Aliases

Subgroups

7902 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7540556);