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C₂²×#2744 #7633506

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

Aliases

Subgroups

7250 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7540702);