#37542800

order	23168
automorphism	?
homology	Abelianization (H₁) = C₂³×C₈ · Schur multiplier (H₂) = C₂⁵

Aliases

No aliases for this group.

Fitting	C₈×Q₈×C₁₈₁ ⋊ C₂
Sylow	C₁₈₁ ⋊ #2982

396 conjugacy classes of subgroups; only the 217 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 217 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=f,b^2=e,c^2=e,f^2=g,b^a=be,d^a=de,c^b=ce,h^d=h^180

3668 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23168, 13589);