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C₂×C₂₃×#464 #15670653

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

500 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 45 points:

(1,2)(23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45);(4,6)(7,8)(9,15)(10,12)(11,19)(13,17)(14,18)(16,22)(20,21);(3,4,5,6)(8,12)(13,21)(14,19)(15,22);(7,9,10,16)(8,13,12,21)(11,20,18,17)(14,22,19,15)

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1766);