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C₄×#2948 #6370077

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

Aliases

Subgroups

3440 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 24 points:

(1,2,3,4);(5,6,8,7)(9,10)(11,15)(12,14)(13,16)(17,20)(18,23)(19,21)(22,24);(10,14)(12,20)(15,21)(16,17)(19,24)(22,23);(5,7,8,6)(9,11)(10,15)(12,19)(13,18)(14,21)(16,23)(17,22)(20,24);(10,16)(11,18)(14,17)(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, 6277273);