C₁₇×C₃⋊D₃×AGL(1,𝔽₁₁) #46778019

order	33660
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅×C₁₇ · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₁₇×C₃⋊D₃×AGL(1,𝔽₁₁)
unambiguous semidirect product	D₁₁⋊(C₅×C₁₇×C₃⋊D₃)
unambiguous semidirect product	(C₃×AGL(1,𝔽₁₁))⋊(D₃×C₁₇)
unambiguous semidirect product	(C₃⋊D₃×D₁₁)⋊(C₅×C₁₇)
unambiguous semidirect product	(C₁₇×C₃⋊D₃×D₁₁)⋊C₅

	subgroup	G/H
center, hypercenter	C₁₇	C₃⋊D₃×AGL(1,𝔽₁₁)
commutator, cosocle, hypocenter	C₃²×C₁₁	C₂²×C₅×C₁₇
Frattini	C₁	G
Fitting, socle	C₃²×C₁₁×C₁₇	C₂²×C₅
LCS	G ▷ C₃²×C₁₁
UCS	C₁ ◁ C₁₇

240 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.

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

μ_t(G) = 1683

1122 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 187);