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C₂²×#2626 #7627710

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

Aliases

Subgroups

17594 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 24 points:

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

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, 7534906);