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C₄×#495 #21689

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

Aliases

Subgroups

575 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

88 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 14677);