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D₇₅₆ #13094139

• metacyclic
• supersolvable
• metabelian
• solvable
• monomial
• stem
• ambivalent

Aliases

Splittings

Subgroups

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 38 points:

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

Polycyclic presentation:

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

Conjugacy classes & character table

381 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1512, 36);