Finite Group Databasebeta

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#2810⋊C₃ #73289

• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

79 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

3,2^7|b^2=f,c^2=fg,d^2=f,e^2=fg,b^a=bc,c^a=bfg,d^a=de,e^a=dfg,f^a=g,g^a=fg,h^a=gh,d^b=dh,e^b=egh,d^c=df,e^c=efh

Conjugacy classes & character table

16 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 5865);