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C₂²×#2836 #7633376

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

Aliases

Subgroups

6334 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7540572);