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C₂²×#2612 #7628036

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

Aliases

Subgroups

7018 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7535232);