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C₂²×#499 #60653

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

Aliases

Subgroups

983 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

88 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 53641);