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C₂²×#2773 #7633563

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

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, 7540759);