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C₄×#2932 #6370034

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

Aliases

Subgroups

3218 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)(9,10,13,17,14,16,22,23)(11,15,19,12,18,20,24,21);(6,8)(9,11)(10,15)(12,17)(13,19)(14,18)(16,20)(21,23)(22,24);(9,12,13,20,14,21,22,15)(10,11,17,19,16,18,23,24);(10,16)(11,18)(17,23)(19,24)

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, 6277230);