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C₂²×#1375 #492840

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

Aliases

Subgroups

1850 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)(9,10,12,17,13,15,21,22,14,18,20,24,11,16,19,23);(6,8)(10,15,18,16)(12,20)(17,23,24,22)(19,21)

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400036);