#13099808

order	1600
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₆ · Schur multiplier (H₂) = C₂²

Aliases

No aliases for this group.

C₅² ⋊ C₂²⋊C₁₆

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₄	D₅×AGL(1,𝔽₅)
commutator	C₂×C₅²	C₂×C₁₆
Fitting	C₂×C₄×C₅²	C₂×C₄
socle	C₂²×C₅²	C₂×C₈
prime radical	C₂²×C₅×D₅	C₈
cosocle	C₂×C₅×#168	C₂²
hypocenter	C₅²	C₂²⋊C₁₆
LCS	G ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂×C₄

143 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 143 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.

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

μ_t(G) = 320

Polycyclic presentation:

2^6,5^2|b^2=c,c^2=e,e^2=f,b^a=bd,h^a=h^4,g^b=g^2,g^c=g^4

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 2160);