Finite Group Databasebeta

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C₂×#5140 #83779

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

368 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 37 points:

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

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 16355);