Q₈⋊(C₆₇⋊C₃₂) #30743308

order	17152
automorphism	?
homology	Abelianization (H₁) = C₂×C₃₂ · Schur multiplier (H₂) = C₂

Aliases

Q₈⋊(C₆₇⋊C₃₂)

C₆₇ ⋊ Q₈⋊C₃₂

118 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 118 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.

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

μ_t(G) = 17152

Polycyclic presentation:

2^8,67|a^2=d,b^2=e,c^2=e,d^2=f,f^2=g,g^2=h,b^a=bc,c^a=ce,i^a=i^66,c^b=ce

2752 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 57045);