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C₂²×#2777 #7633548

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

Aliases

Subgroups

6726 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7540744);