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C₂²×#1793 #6370741

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

Aliases

Subgroups

17274 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 24 points:

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

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, 6277937);