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C₂²×#2330 #7625298

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

Aliases

Subgroups

8586 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7532494);