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C₂×C₂₃×#576 #15671200

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1512 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 41 points:

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

Conjugacy classes & character table

1012 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 2313);