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C₂×#4519 #71457

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 37 points:

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

Conjugacy classes & character table

60 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 4033);