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C₂²×#1907 #6371530

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

Aliases

Subgroups

6722 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)(9,10,14,16,13,12,18,21)(11,17,19,24,20,15,22,23);(9,11,18,19,13,20,14,22)(10,15,16,24,12,17,21,23);(6,8)(9,12)(10,13)(11,17)(14,16)(15,20)(18,21)(19,23)(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, 6278726);