D₁₇₃⋊#364 #36369902

order	22144
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂²

Aliases

D₁₇₃⋊#364

C₁₇₃ ⋊ C₂×#364

168 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.

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

μ_t(G) = 2768

Polycyclic presentation:

2^7,173|a^2=e,b^2=d,d^2=g,e^2=f,f^2=g,b^a=bd,d^a=dg,h^a=h^80,h^c=h^172,h^e=h^172

1432 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22144, 20849);