D₅×C₁₁×C₃⋊AGL(1,𝔽₁₁) #49137488

order	36300
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅×C₁₁ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₅×C₁₁×C₃⋊AGL(1,𝔽₁₁)
unambiguous semidirect product	(C₃×D₅)⋊(C₁₁×AGL(1,𝔽₁₁))
unambiguous semidirect product	(D₅×C₁₁⋊C₅)⋊(D₃×C₁₁)
unambiguous semidirect product	(D₅×D₃₃)⋊(C₅×C₁₁)

	subgroup	G/H
center, hypercenter	C₁₁	D₅×C₃⋊AGL(1,𝔽₁₁)
commutator, cosocle, hypocenter	C₃×C₅×C₁₁	C₂²×C₅×C₁₁
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₁²	C₂²×C₅
LCS	G ▷ C₃×C₅×C₁₁
UCS	C₁ ◁ C₁₁

200 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.

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

μ_t(G) = 1650

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36300, 624);