#44552196

order	32128
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂²

Aliases

No aliases for this group.

Fitting	C₄⋊C₁₆×C₂₅₁ ⋊ C₂
Sylow	C₂₅₁ ⋊ #2169

162 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 71 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=e,c^2=e,e^2=f,f^2=g,b^a=bd,c^a=cg,c^b=cg,h^b=h^250,h^c=h^250

5056 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32128, 6341);