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C₄×#1772 #353242

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

Aliases

Subgroups

1494 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 260438);