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C₂²×#2743 #7633504

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

Aliases

Subgroups

8818 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)(13,14)(15,16)(17,18)(19,20)(21,22)(23,26)(24,28)(25,27);(6,7)(8,12)(14,18)(16,20)(21,23,25,28)(22,26,27,24);(5,7,9,6)(8,11,12,10)(13,15,17,19)(14,16,18,20)(21,23)(22,24)(25,28)(26,27);(5,8)(6,10)(7,11)(9,12)(13,16)(14,19)(15,18)(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, 7540700);