#37534975

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

Aliases

No aliases for this group.

Fitting	C₂×#100×C₁₈₁ ⋊ C₂
Sylow	C₁₈₁ ⋊ #2045

296 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 67 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|c^2=d,d^2=g,b^a=bd,c^a=ce,d^a=dg,c^b=cf,d^b=dg,h^b=h^180,e^c=eg,f^c=fg

2006 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23168, 5764);