#28392479

order	14464
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

C₁₁₃ ⋊ #2183

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₁₁₃
commutator, socle, prime radical	C₂²×C₁₁₃	C₂²×C₈
Fitting	C₄⋊C₁₆×C₁₁₃	C₂
cosocle	C₂×C₈×C₁₁₃	C₂³
hypercenter	C₄⋊C₁₆	D₁₁₃
hypocenter	C₁₁₃	#2183
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₄⋊C₁₆

126 conjugacy classes of subgroups.

μ_t(G) = 14464

Polycyclic presentation:

2^7,113|a^2=e,b^2=d,c^2=de,e^2=f,f^2=g,b^a=bd,c^a=cg,h^c=h^112

2296 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 6415);