D₄⋊(C₂₇₁⋊C₁₆) #46834319

order	34688
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₆ · Schur multiplier (H₂) = C₂²

Aliases

D₄⋊(C₂₇₁⋊C₁₆)

C₂₇₁ ⋊ D₄⋊C₁₆

110 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 110 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

μ_t(G) = 17344

Polycyclic presentation:

2^7,271|a^2=d,c^2=e,d^2=f,f^2=g,b^a=bc,c^a=ce,h^a=h^270,c^b=ce

5456 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34688, 2465);