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C₄×#562 #34352

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

Aliases

Subgroups

1124 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 20 points:

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

Conjugacy classes & character table

76 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 27340);