#37533488

order	23168
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂²×C₄

Aliases

No aliases for this group.

Fitting	C₂×C₄×C₈×C₁₈₁ ⋊ C₂
Sylow	C₁₈₁ ⋊ #1750

336 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 129 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=e,b^2=f,c^2=e,f^2=g,b^a=bd,c^a=cg,h^a=h^180

5816 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23168, 4277);