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C₂×C₁₉×#473 #14560923

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

448 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 53 points:

(1,2)(35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53);(3,4,9,14)(5,15,19,25)(6,20,22,28)(7,13,8,12)(10,18,26,17)(11,23,27,21)(16,30,32,24)(29,33,34,31);(3,5,8,18,9,19,7,17)(4,10,13,25,14,26,12,15)(6,16,23,33,22,32,21,31)(11,24,28,34,27,30,20,29);(3,6)(4,11)(5,16)(7,21)(8,23)(9,22)(10,24)(12,20)(13,28)(14,27)(15,29)(17,31)(18,33)(19,32)(25,34)(26,30)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1798);