#32989236

order	18688
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂⁴

Aliases

No aliases for this group.

	subgroup	G/H
center	C₂²	#17988498
commutator, prime radical, cosocle	C₂⁵×C₇₃	C₂³
Frattini	C₂⁵	C₂²×D₇₃
Fitting	C₇₃×#2840	C₂
socle	C₂²×C₇₃	#393
hypercenter	#2840	D₇₃
hypocenter	C₇₃	#10391
LCS	G ▷ C₂⁵×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂⁵ ◁ #2840

542 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.

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

μ_t(G) = 2336

Polycyclic presentation:

2^8,73|a^2=d,b^2=d,c^2=h,b^a=bd,c^a=ce,e^a=eg,f^a=fgh,c^b=cf,e^b=eh,f^b=fg,d^c=dg,i^c=i^72

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 72820);