Finite Group Databasebeta

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C₃×#90342 #13060997

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

392 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 34 points:

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

Conjugacy classes & character table

183 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 10286);