#16780872

order	3328
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂×C₄

Aliases

No aliases for this group.

C₁₃ ⋊ #8263

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×#261
commutator, socle, prime radical	C₂³×C₁₃	C₂×C₄²
Fitting	C₁₃×#336	C₄
cosocle	C₂×C₄×Dic₁₃	C₂³
hypercenter	#336	#261
hypocenter	C₁₃	#8263
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ #336

470 conjugacy classes of subgroups.

μ_t(G) = 3328

Polycyclic presentation:

2^8,13|a^2=e,b^2=f,c^2=de,e^2=g,f^2=h,b^a=bd,c^a=cg,i^a=i^8,c^b=ch,i^c=i^8,i^e=i^12

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1087521);