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C₂²×#491 #60608

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

Aliases

Subgroups

1071 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

64 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 53596);