#37548809

order	23168
automorphism	?
homology	Abelianization (H₁) = C₄² · Schur multiplier (H₂) = C₂×C₄

Aliases

No aliases for this group.

Fitting	C₂²×C₈×C₁₈₁ ⋊ C₄
Sylow	C₁₈₁ ⋊ #1391

166 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 166 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.

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

μ_t(G) = 5792

Polycyclic presentation:

2^7,181|a^2=d,b^2=e,e^2=g,b^a=bc,c^a=cf,f^a=fg,h^a=h^162,d^b=df,d^c=dg,h^d=h^180

1466 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23168, 19598);