#13103951

order	1600
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

C₅² ⋊ #446

	subgroup	G/H
center, Frattini	C₂²	C₂×D₅⋊AGL(1,𝔽₅)
commutator, socle, prime radical	C₂²×C₅²	C₂²×C₄
Fitting	C₂×C₄×C₅²	C₂×C₄
cosocle	C₂×#1039	C₂³
hypercenter	C₂×C₄	D₅⋊AGL(1,𝔽₅)
hypocenter	C₅²	#446
LCS	G ▷ C₂²×C₅² ▷ C₅²
UCS	C₁ ◁ C₂² ◁ C₂×C₄

232 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 67 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|a^2=d,b^2=ef,c^2=ef,d^2=f,b^a=be,g^a=g^2,h^a=h^2,c^b=cef,g^b=g^4,g^d=g^4,h^d=h^4

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 6303);