#37532875

order	23168
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

No aliases for this group.

Fitting	D₄⋊C₈×C₁₈₁ ⋊ C₂
Sylow	C₁₈₁ ⋊ #1635

234 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.

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

μ_t(G) = 11584

Polycyclic presentation:

2^7,181|a^2=f,b^2=g,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^180,d^b=df,e^b=eg,h^b=h^180,d^c=dg,e^c=eg,h^c=h^180

2546 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23168, 3664);