Finite Group Databasebeta

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#2845⋊C₃ #73295

• solvable
• stem

Aliases

Splittings

Subgroups

75 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 24 points:

(1,2,6)(3,10,15)(4,13,16)(5,7,17)(8,18,14)(9,20,12)(11,21,24)(19,23,22);(1,4)(3,22)(5,14)(6,16,17,18)(8,13)(9,10)(11,12)(15,24,20,23);(1,12,5,3)(2,9,7,10)(4,11,14,22)(6,17)(8,21,13,19)(15,20)

Polycyclic presentation:

3,2^7|b^2=g,c^2=gh,d^2=fh,e^2=f,b^a=be,c^a=df,d^a=cdfgh,e^a=bf,f^a=g,g^a=fg,h^a=gh,c^b=cf,d^b=dfg,d^c=dfgh,e^c=eg,e^d=ef

Conjugacy classes & character table

14 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 5871);