#10600276

order	640
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂²

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₅
commutator, socle, prime radical	C₂³×C₅	C₂²×C₄
Fitting	C₄×C₅×C₄⋊C₄	C₂
cosocle	C₂²×C₄×C₅	C₂³
hypercenter	C₄×C₄⋊C₄	D₅
hypocenter	C₅	#1917
LCS	G ▷ C₂³×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×C₄⋊C₄

228 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.

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

μ_t(G) = 640

Polycyclic presentation:

2^7,5|a^2=f,b^2=f,c^2=d,f^2=g,b^a=bd,c^a=ce,h^a=h^4,c^b=cg,h^b=h^4

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(640, 2358);