#13104171

order	1600
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

No aliases for this group.

C₅² ⋊ #400

	subgroup	G/H
center, Frattini	C₂²	C₂×D₅²⋊C₂
commutator, prime radical, cosocle	C₂²×C₅⋊D₅	C₂³
Fitting	C₂×C₄×C₅²	D₄
socle	C₂²×C₅²	C₂×D₄
hypercenter	C₂×C₄	D₅²⋊C₂
hypocenter	C₅²	#400
LCS	G ▷ C₂²×C₅⋊D₅ ▷ C₅²
UCS	C₁ ◁ C₂² ◁ C₂×C₄

264 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 41 normal subgroups are shown.

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

μ_t(G) = 80

Polycyclic presentation:

2^6,5^2|a^2=f,b^2=de,c^2=e,b^a=bd,c^a=cf,g^a=g^4,h^a=g^2h,c^b=cef,g^b=g^3h^3,h^b=h^2,g^d=g^4,h^d=h^4

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 6523);