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C₂×#1426 #13637

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

Aliases

Subgroups

95 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 34 points:

(1,2);(4,9,11,22)(5,14)(6,18)(7,19)(10,25)(12,26,29,34)(13,32,30,24)(15,20)(16,28)(17,27)(21,33,31,23);(3,4,10,26,6,12,5,9,19,30,14,23,15,21,25,32,8,11,28,34,20,29,17,22,7,13,27,33,18,31,16,24)

Conjugacy classes & character table

52 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 6625);