SD₁₆⋊(C₁₆₇⋊C₈) #36322951

order	21376
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂²

Aliases

SD₁₆⋊(C₁₆₇⋊C₈)

C₁₆₇ ⋊ SD₁₆⋊C₈

176 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.

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

μ_t(G) = 10688

Polycyclic presentation:

2^7,167|a^2=e,c^2=e,d^2=f,e^2=g,b^a=bd,c^a=cf,d^a=df,h^a=h^166,d^b=df,h^c=h^166

2368 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21376, 3323);