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C₂²×#1593 #6344580

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

Aliases

Subgroups

1882 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 28 points:

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

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, 6251776);