Finite Group Databasebeta

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C₅×#80230 #14424531

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1400 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 44 points:

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

Conjugacy classes & character table

255 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 150229);