#37548761

order	23168
automorphism	?
homology	Abelianization (H₁) = C₄×C₈ · Schur multiplier (H₂) = C₂²

Aliases

No aliases for this group.

Fitting	C₂×C₁₆×C₁₈₁ ⋊ C₄
Sylow	C₁₈₁ ⋊ #1375

140 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 56 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,c^2=g,d^2=f,f^2=g,b^a=bc,e^a=eg,d^b=dg,h^b=h^162,h^e=h^180

1484 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23168, 19550);