#18085505

order	4864
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

	subgroup	G/H
center	C₂²	#11926454
commutator, prime radical, cosocle	C₂⁵×C₁₉	C₂³
Frattini	C₂⁵	C₂²×D₁₉
Fitting	C₁₉×#1304	C₂
socle	C₂²×C₁₉	#392
hypercenter	#1304	D₁₉
hypocenter	C₁₉	#10339
LCS	G ▷ C₂⁵×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂⁵ ◁ #1304

738 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.

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

μ_t(G) = 608

Polycyclic presentation:

2^8,19|a^2=g,b^2=g,c^2=h,b^a=bd,c^a=ce,f^a=fgh,i^a=i^18,c^b=cf,e^b=eh,i^b=i^18,d^c=dg,i^c=i^18

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 72534);