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C₂²×#3380 #10576195

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

Aliases

Subgroups

6994 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10483391);