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C₄×#3280 #6383802

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

Aliases

Subgroups

2998 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)(9,10,13,15)(11,17,20,24)(12,21,22,16)(14,18,23,19);(9,11)(10,14)(12,18)(13,20)(15,23)(16,24)(17,21)(19,22);(6,8);(10,15)(11,18)(12,22)(14,17)(19,20)(23,24)

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6290998);