C₃⋊(C₇⋊(C₁₁⋊#1042)) #37528673

order	23100
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

unambiguous semidirect product	C₃⋊(C₇⋊(C₁₁⋊#1042))
unambiguous semidirect product	C₇⋊(C₃⋊(C₁₁⋊#1042))
unambiguous semidirect product	C₁₁⋊(C₃⋊(C₇⋊#1042))

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₅²×C₇×C₁₁	C₄
prime radical, cosocle	C₃×C₅×C₇×D₅×C₁₁	C₂
LCS	G ▷ C₃×C₅²×C₇×C₁₁
UCS	C₁

104 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 104 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.

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

μ_t(G) = 4620

Polycyclic presentation:

2^2,3,5^2,7,11|a^2=b,c^a=c^2,d^a=d^2,e^a=e^4,f^a=f^6,g^a=g^10,d^b=d^4

2313 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 484);