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C₄×#3500 #7625672

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

Aliases

Subgroups

11234 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)(11,17)(12,20)(13,14)(15,19)(16,21)(18,22)(23,24);(10,14)(15,17)(16,20)(22,23);(5,6,7,8)(9,11)(10,15)(12,18)(13,19)(14,17)(16,22)(20,23)(21,24);(9,10)(11,15)(12,16)(13,14)(17,19)(18,22)(20,21)(23,24);(9,12,13,21)(10,16,14,20)(11,18,19,24)(15,22,17,23)

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, 7532868);