C₃⋊(ΓL(1,𝔽₈)⋊Dic₆₅) #30655247

order	16380
automorphism	?
homology	Abelianization (H₁) = C₃×C₄ · Schur multiplier (H₂) = C₁

Aliases

unambiguous semidirect product	C₃⋊(ΓL(1,𝔽₈)⋊Dic₆₅)
unambiguous semidirect product	ΓL(1,𝔽₈)⋊Dic₁₉₅

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

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

normal subgroups only

This group has 112 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) = 5460

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 297);