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C₂²×#2647 #7627773

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

Aliases

Subgroups

6306 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7534969);