D₁₀₉⋊(D₄⋊C₈) #28378318

order	13952
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂⁴

Aliases

D₁₀₉⋊(D₄⋊C₈)

C₁₀₉ ⋊ C₂×D₄⋊C₈

344 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.

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

μ_t(G) = 3488

Polycyclic presentation:

2^7,109|a^2=e,d^2=f,e^2=g,b^a=bd,d^a=df,h^a=h^33,d^b=df,h^c=h^108,h^e=h^108

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 19796);