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C₂²×#3007 #10574861

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

Aliases

Subgroups

23494 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 10482057);