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C₂²×#1387 #492875

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

Aliases

Subgroups

1810 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 24 points:

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

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, 400071);