#35227670

order	20864
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁵

Aliases

No aliases for this group.

Fitting	C₂×#135×C₁₆₃ ⋊ C₂
Sylow	C₁₆₃ ⋊ #3414

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

normal subgroups only

This group has 364 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) = 5216

Polycyclic presentation:

2^7,163|d^2=g,e^2=fg,f^2=g,b^a=be,c^a=cg,e^a=ef,f^a=fg,e^b=ef,f^b=fg,h^b=h^162

2300 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20864, 17644);