#37543588

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

Aliases

No aliases for this group.

Fitting	C₂×#106×C₁₈₁ ⋊ C₂
Sylow	C₁₈₁ ⋊ #3084

376 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 133 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=eg,b^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^180,d^b=dg,h^b=h^180,f^c=fg,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, 14377);