#13099345

order	1600
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

C₅² ⋊ #352

	subgroup	G/H
center	C₂	#11716621
commutator	C₂³×C₅²	C₂×C₄
Frattini, hypercenter	C₂×D₄	D₅²
Fitting, prime radical, cosocle	C₂×C₅²×D₄	C₂²
socle	C₂×C₅²	#99
hypocenter	C₅²	#352
LCS	G ▷ C₂³×C₅² ▷ C₂²×C₅² ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×D₄

182 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 182 conjugacy classes of subgroups — too many to draw. Only its 38 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=c,b^a=bd,c^a=ce,h^a=h^4,d^b=de,e^b=ef,g^b=g^4,d^c=df

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 1697);