#44551365

order	32128
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂⁴

Aliases

No aliases for this group.

Fitting	C₂²×SD₁₆×C₂₅₁ ⋊ C₂
Sylow	C₂₅₁ ⋊ #2000

444 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

μ_t(G) = 16064

Polycyclic presentation:

2^7,251|a^2=g,d^2=g,b^a=bd,c^a=ce,d^a=dg,c^b=cf,d^b=dg,h^c=h^250

3532 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32128, 5510);