#37534854

order	23168
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂⁴

Aliases

No aliases for this group.

Fitting	C₂×C₄⋊Q₈×C₁₈₁ ⋊ C₂
Sylow	C₁₈₁ ⋊ #2023

326 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 95 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=d,b^2=d,e^2=g,b^a=bd,c^a=ce,e^a=eg,c^b=cf,e^c=eg,h^c=h^180

2552 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23168, 5643);