C₃⋊(ΓL(1,𝔽₈)⋊(Dic₁₁⋊C₅)) #28357476

order	13860
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₅ · Schur multiplier (H₂) = C₁

Aliases

unambiguous semidirect product	C₃⋊(ΓL(1,𝔽₈)⋊(Dic₁₁⋊C₅))
unambiguous semidirect product	ΓL(1,𝔽₈)⋊(C₃⋊(Dic₁₁⋊C₅))
unambiguous semidirect product	(C₁₁⋊C₅)⋊(C₃⋊(ΓL(1,𝔽₈)⋊C₄))
unambiguous semidirect product	(C₃⋊(C₁₁⋊(ΓL(1,𝔽₈)⋊C₄)))⋊C₅
unambiguous semidirect product	(C₃⋊(C₇⋊(Dic₁₁⋊C₅)))⋊C₃

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₃⋊(ΓL(1,𝔽₈)⋊AGL(1,𝔽₁₁))
commutator, hypocenter	C₃×C₇×C₁₁	C₃×C₄×C₅
Fitting, socle, cosocle	C₂×C₃×C₇×C₁₁	C₂×C₃×C₅
prime radical	C₂×C₃×ΓL(1,𝔽₈)×C₁₁⋊C₅	C₂
LCS	G ▷ C₃×C₇×C₁₁
UCS	C₁ ◁ C₂

112 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.

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

μ_t(G) = 924

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13860, 143);