C₃⋊(SL(2,𝔽₃)⋊C₁₆) #11920140

order	1152
automorphism	?
homology	Abelianization (H₁) = C₁₆ · Schur multiplier (H₂) = C₃

Aliases

unambiguous semidirect product	C₃⋊(SL(2,𝔽₃)⋊C₁₆)
unambiguous semidirect product	SL(2,𝔽₃)⋊(C₃⋊C₁₆)

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₈	C₃⋊S₄
commutator, hypocenter	C₃×SL(2,𝔽₃)	C₁₆
Fitting	C₃×C₈×Q₈	D₃
socle	C₂²×C₃	A₄⋊C₈
prime radical	C₂×C₃×SL(2,𝔽₃)	C₈
cosocle	C₃×C₈×SL(2,𝔽₃)	C₂
LCS	G ▷ C₃×SL(2,𝔽₃)
UCS	C₁ ◁ C₂×C₈

146 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.

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

μ_t(G) = 384

Polycyclic presentation:

2^4,3^2,2^3|a^2=b,b^2=c,c^2=d,g^2=i,h^2=i,e^a=e^2,f^a=f^2,g^a=gh,h^a=hi,g^e=h,h^e=ghi,h^g=hi

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 154151);