#44548746

order	32128
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

Fitting	Q₈⋊C₈×C₂₅₁ ⋊ C₂
Sylow	C₂₅₁ ⋊ #1476

276 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 85 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=f,d^2=f,e^2=g,b^a=bd,d^a=df,d^b=df,h^b=h^250,h^c=h^250

3556 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32128, 2891);