D₁₄₉⋊#364 #34061030

order	19072
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂²

Aliases

D₁₄₉⋊#364

C₁₄₉ ⋊ 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) = 2384

Polycyclic presentation:

2^7,149|a^2=e,b^2=d,d^2=g,e^2=f,f^2=g,b^a=bd,d^a=dg,h^a=h^105,h^c=h^148,h^e=h^148

1240 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19072, 20849);