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C₇⋊(C₉⋊C₈) #92579

• metacyclic
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 24 points:

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

Polycyclic presentation:

2^3,3,7,3|a^2=b,b^2=c,d^3=f^2,d^a=d^2f,e^a=e^6,f^a=f^2

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(504, 5);