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C₂²×#2508 #7627943

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

Aliases

Subgroups

6698 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7535139);