#14273045

order	1872
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₁

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃²⋊D₁₃
commutator, cosocle	C₁₃×C₃⋊Dic₃	C₂²
Fitting, socle	C₂×C₃²×C₁₃	D₄
prime radical	C₁₃×#625	C₂
hypocenter	C₃²×C₁₃	SD₁₆
LCS	G ▷ C₁₃×C₃⋊Dic₃ ▷ C₂×C₃²×C₁₃ ▷ C₃²×C₁₃
UCS	C₁ ◁ C₂

68 conjugacy classes of subgroups.

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 312

Polycyclic presentation:

2^4,3^2,13|a^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^2,f^a=e^2f,g^a=g^12,c^b=cd,e^b=e^2f^2,e^c=e^2,f^c=f^2

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1872, 673);