#13097232

order	1584
isoclinism	isoclinic class of #157⋊D₁₁
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂²

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini, hypercenter	C₂	#157⋊D₁₁
commutator	C₁₁×C₃⋊D₃	C₂×C₄
Fitting, socle	C₂×C₃²×C₁₁	D₄
prime radical	C₂×(C₃⋊D₃)⋊D₁₁	C₂
cosocle	C₂×C₁₁×C₃⋊D₃	C₂²
hypocenter	C₃²×C₁₁	C₂²⋊C₄
LCS	G ▷ C₁₁×C₃⋊D₃ ▷ C₃²×C₁₁
UCS	C₁ ◁ C₂

116 conjugacy classes of subgroups; only the 21 normal subgroups are shown.

normal subgroups only

This group has 116 conjugacy classes of subgroups — too many to draw. Only its 21 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

μ_t(G) = 132

Polycyclic presentation:

2^4,3^2,11|b^2=cd,b^a=bc,e^a=e^2,g^a=g^10,e^b=f,f^b=e^2,e^c=e^2,f^c=f^2

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1584, 396);