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C₄×#2825 #544347

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

Aliases

Subgroups

3012 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 28 points:

(1,2,3,4);(5,6,8,11)(7,10,12,9)(13,14)(15,17)(16,18)(19,20)(21,22,24,26)(23,25,27,28);(5,7)(6,9)(8,12)(10,11)(13,15)(14,17)(16,19)(18,20)(21,23)(22,25)(24,27)(26,28);(5,7)(6,10)(8,12)(9,11)(14,18)(17,20)(23,27)(25,28);(7,12)(9,10)(15,19)(17,20)

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 451543);