#13100022

order	1600
isoclinism	isoclinic class of #6057
automorphism	?
homology	Abelianization (H₁) = C₄×C₈ · Schur multiplier (H₂) = C₂³×C₅

Aliases

No aliases for this group.

C₅² ⋊ #336

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₄	#6057
commutator	C₅⋊D₅	C₄×C₈
Fitting	C₂×C₄×C₅²	Q₈
socle	C₂²×C₅²	C₄⋊C₄
prime radical	C₂²×C₅⋊D₅	C₂×C₄
cosocle	C₂×C₄×C₅⋊D₅	C₂²
hypocenter	C₅²	#336
LCS	G ▷ C₅⋊D₅ ▷ C₅²
UCS	C₁ ◁ C₂×C₄

248 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 49 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=c,b^2=ce,c^2=f,d^2=f,b^a=bcdf,g^a=g^2,h^a=h^3,g^b=h,h^b=g^4,g^c=g^4,h^c=h^4

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 2374);