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C₂²×#3147 #10575233

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

Aliases

Subgroups

13178 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 10482429);