ΓL(1,𝔽₈)⋊(Dic₆₅⋊C₃) #30655191

order	16380
automorphism	?
homology	Abelianization (H₁) = C₃²×C₄ · Schur multiplier (H₂) = C₃

Aliases

unambiguous semidirect product	ΓL(1,𝔽₈)⋊(Dic₆₅⋊C₃)
unambiguous semidirect product	#19129703⋊C₃
unambiguous semidirect product	(ΓL(1,𝔽₈)⋊Dic₆₅)⋊C₃
unambiguous semidirect product	#19129705⋊C₃
unambiguous semidirect product	#19129706⋊C₃

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₅⋊(ΓL(1,𝔽₈)⋊(D₁₃⋊C₃))
commutator, hypocenter	C₅×C₇×C₁₃	C₃²×C₄
Fitting, socle, cosocle	C₂×C₅×C₇×C₁₃	C₂×C₃²
prime radical	C₂×C₅×ΓL(1,𝔽₈)×C₁₃⋊C₃	C₂
LCS	G ▷ C₅×C₇×C₁₃
UCS	C₁ ◁ C₂

144 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.

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

μ_t(G) = 1820

Polycyclic presentation:

2,3^2,5,7,13,2|a^2=g,d^a=d^4,e^a=e^6,f^a=f^12,f^b=f^3,e^c=e^2

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 241);