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C₂²×#2532 #7627963

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

Aliases

Subgroups

7438 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)(14,15)(16,20)(23,27)(26,28);(6,7)(10,11)(13,14,17,15)(16,18,20,19)(21,22,25,24)(23,26,27,28);(5,7,9,6)(8,11,12,10)(13,15,17,14)(16,19,20,18)(21,23)(22,26)(24,28)(25,27);(5,8,9,12)(6,10,7,11)(13,16)(14,18)(15,19)(17,20)(21,24,25,22)(23,28,27,26)

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, 7535159);