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C₄×#3543 #7626189

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

Aliases

Subgroups

8482 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 20 points:

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7533385);