#28378961

order	13952
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂²

Aliases

No aliases for this group.

C₁₀₉ ⋊ #1840

	subgroup	G/H
center, Frattini	C₂³	C₂²×#89137
commutator, socle, prime radical	C₂³×C₁₀₉	C₂²×C₄
Fitting	#95×C₁₀₉	C₄
cosocle	C₂²×Dic₁₀₉	C₂³
hypercenter	#95	#89137
hypocenter	C₁₀₉	#1840
LCS	G ▷ C₂³×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂³ ◁ #95

196 conjugacy classes of subgroups.

μ_t(G) = 13952

Polycyclic presentation:

2^7,109|a^2=f,b^2=de,c^2=d,f^2=g,b^a=bd,c^a=ce,h^a=h^33,c^b=cg,h^f=h^108

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 20439);