C₃×C₅×ΓL(1,𝔽₈)×AGL(1,𝔽₁₁) #46831537

order	34650
automorphism	?
homology	Abelianization (H₁) = C₂×C₃²×C₅² · Schur multiplier (H₂) = C₃×C₅

Aliases

direct product	C₃×C₅×ΓL(1,𝔽₈)×AGL(1,𝔽₁₁)
unambiguous semidirect product	D₁₁⋊(C₃×C₅²×ΓL(1,𝔽₈))
unambiguous semidirect product	(C₁₁⋊C₅)⋊(C₂×C₃×C₅×ΓL(1,𝔽₈))
unambiguous semidirect product	(C₃×D₁₁)⋊(C₅²×ΓL(1,𝔽₈))
unambiguous semidirect product	(C₅×D₁₁)⋊(C₃×C₅×ΓL(1,𝔽₈))
unambiguous semidirect product	(C₃×C₅×D₁₁)⋊(C₅×ΓL(1,𝔽₈))
unambiguous semidirect product	(ΓL(1,𝔽₈)×D₁₁)⋊(C₃×C₅²)
unambiguous semidirect product	(C₇×AGL(1,𝔽₁₁))⋊(C₃²×C₅)
unambiguous semidirect product	(C₃×ΓL(1,𝔽₈)×D₁₁)⋊C₅²
unambiguous semidirect product	(C₃×C₇×AGL(1,𝔽₁₁))⋊(C₃×C₅)
unambiguous semidirect product	(C₅×ΓL(1,𝔽₈)×D₁₁)⋊(C₃×C₅)
unambiguous semidirect product	(C₅×C₇×AGL(1,𝔽₁₁))⋊C₃²
unambiguous semidirect product	(C₃×C₅×ΓL(1,𝔽₈)×D₁₁)⋊C₅
unambiguous semidirect product	(C₃×C₅×C₇×AGL(1,𝔽₁₁))⋊C₃

	subgroup	G/H
center, hypercenter	C₃×C₅	ΓL(1,𝔽₈)×AGL(1,𝔽₁₁)
commutator, cosocle, hypocenter	C₇×C₁₁	C₂×C₃²×C₅²
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₁₁	C₂×C₃×C₅
LCS	G ▷ C₇×C₁₁
UCS	C₁ ◁ C₃×C₅

384 conjugacy classes of subgroups; only the 144 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 144 normal subgroups are shown.

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

μ_t(G) = 1155

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 180);