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C₄×#1899 #354273

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

Aliases

Subgroups

2336 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 24 points:

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 261469);