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C₄×#2050 #359102

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

Aliases

Subgroups

1454 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 20 points:

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

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, 266298);