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C₂²×#2809 #7633601

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

Aliases

Subgroups

6626 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7540797);