D₂₉₃⋊#361 #49175109

order	37504
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³

Aliases

D₂₉₃⋊#361

C₂₉₃ ⋊ C₂×#361

256 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.

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

μ_t(G) = 4688

Polycyclic presentation:

2^7,293|a^2=e,d^2=f,e^2=g,f^2=g,b^a=bd,d^a=df,f^a=fg,h^a=h^138,d^b=dfg,e^b=eg,f^b=fg,h^c=h^292,h^e=h^292

1054 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37504, 20834);