C₃⋊(ΓL(1,𝔽₈)⋊(D₁₁⋊C₂₅)) #46831398

order	34650
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₂₅ · Schur multiplier (H₂) = C₁

Aliases

unambiguous semidirect product	C₃⋊(ΓL(1,𝔽₈)⋊(D₁₁⋊C₂₅))
unambiguous semidirect product	ΓL(1,𝔽₈)⋊(C₃⋊(D₁₁⋊C₂₅))
unambiguous semidirect product	(C₁₁⋊C₂₅)⋊(C₃⋊AGL(1,𝔽₇))
unambiguous semidirect product	(C₃⋊(C₁₁⋊AGL(1,𝔽₇)))⋊C₂₅
unambiguous semidirect product	(C₃⋊(C₇⋊(D₁₁⋊C₂₅)))⋊C₃

	subgroup	G/H
center, Frattini, hypercenter	C₅	C₃⋊(ΓL(1,𝔽₈)⋊AGL(1,𝔽₁₁))
commutator, hypocenter	C₃×C₇×C₁₁	C₂×C₃×C₂₅
Fitting, socle, cosocle	C₃×C₅×C₇×C₁₁	C₂×C₃×C₅
prime radical	C₅×C₃⋊(C₁₁⋊AGL(1,𝔽₇))	C₅
LCS	G ▷ C₃×C₇×C₁₁
UCS	C₁ ◁ C₅

108 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 108 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.

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

μ_t(G) = 5775

Polycyclic presentation:

2,3,5,3,7,11,5|c^5=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(34650, 41);