#63070⋊C₅ #13046068

order	1280
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₂

Aliases

	subgroup	G/H
center, Frattini, socle	C₂²	C₂²×C₂⁴⋊C₅
commutator, cosocle, hypocenter	#564	C₂²×C₅
Fitting	#63070	C₅
hypercenter	C₂×Q₈	C₂⁴⋊C₅
LCS	G ▷ #564
UCS	C₁ ◁ C₂² ◁ C₂×Q₈

702 conjugacy classes of subgroups; only the 29 normal subgroups are shown.

normal subgroups only

This group has 702 conjugacy classes of subgroups — too many to draw. Only its 29 normal subgroups are shown.

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

μ_t(G) = 256

Polycyclic presentation:

5,2^8|b^2=hi,c^2=h,d^2=hi,e^2=h,f^2=i,g^2=i,b^a=be,c^a=e,d^a=bchi,e^a=cd,c^b=ch,d^b=di,e^b=eh,d^c=dhi,e^c=ei,g^f=gi

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1116336);