#34013867

order	18688
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂²

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×#64408
commutator, socle, prime radical	C₂³×C₇₃	C₂²×C₈
Fitting	C₄×C₄⋊C₄×C₇₃	C₄
cosocle	C₂²×#10596831	C₂³
hypercenter	C₄×C₄⋊C₄	#64408
hypocenter	C₇₃	#13160
LCS	G ▷ C₂³×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×C₄⋊C₄

338 conjugacy classes of subgroups.

μ_t(G) = 18688

Polycyclic presentation:

2^8,73|a^2=f,b^2=f,c^2=e,f^2=g,g^2=h,b^a=bd,c^a=ce,i^a=i^27,c^b=ch,i^b=i^27,i^f=i^72

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 1097451);