#44549478

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

Aliases

No aliases for this group.

Fitting	Q₈⋊C₈×C₂₅₁ ⋊ C₂
Sylow	C₂₅₁ ⋊ #1628

216 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 53 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|b^2=g,c^2=fg,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^250,d^b=df,e^b=eg,h^b=h^250,d^c=dg,e^c=eg,h^c=h^250

3526 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32128, 3623);