#15890338

order	3328
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁶

Aliases

No aliases for this group.

	subgroup	G/H
center	C₂²	C₂×#88136
commutator, prime radical, cosocle	C₂⁴×C₁₃	C₂⁴
Frattini	C₂⁴	C₂³×D₁₃
Fitting	C₁₃×#1740	C₂
socle	C₂²×C₁₃	C₂×#120
hypercenter	#1740	D₁₃
hypocenter	C₁₃	#23470
LCS	G ▷ C₂⁴×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #1740

1178 conjugacy classes of subgroups.

μ_t(G) = 832

Polycyclic presentation:

2^8,13|a^2=e,b^2=e,c^2=h,d^2=h,b^a=be,c^a=cf,g^a=gh,c^b=cg,f^b=fh,i^b=i^12,d^c=dh,i^c=i^12

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 196987);