ΓL(1,𝔽₈)⋊((C₁₁⋊C₅)⋊Dic₅) #37528332

order	23100
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₅ · Schur multiplier (H₂) = C₁

Aliases

unambiguous semidirect product	ΓL(1,𝔽₈)⋊((C₁₁⋊C₅)⋊Dic₅)
unambiguous semidirect product	(C₁₁⋊C₅)⋊(ΓL(1,𝔽₈)⋊Dic₅)
unambiguous semidirect product	(C₁₁⋊(ΓL(1,𝔽₈)⋊Dic₅))⋊C₅
unambiguous semidirect product	(C₇⋊((C₁₁⋊C₅)⋊Dic₅))⋊C₃

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

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

normal subgroups only

This group has 128 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) = 1540

Polycyclic presentation:

2,3,5^2,7,11,2|a^2=g,d^a=d^4,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(23100, 143);