C₂×C₃⋊(#458⋊C₃) #11921375

order	1152
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product	C₂×C₃⋊(#458⋊C₃)
unambiguous semidirect product	(C₂×C₃)⋊(#458⋊C₃)
unambiguous semidirect product	(C₂×#5243)⋊C₃

	subgroup	G/H
center, hypercenter	C₂²	C₃⋊(#120⋊C₃)
commutator, cosocle, hypocenter	C₃×H(5,𝔽₂)	C₂²×C₃
Frattini	C₂³	C₂×D₃×A₄
Fitting	C₂×C₃×H(5,𝔽₂)	C₂×C₃
socle	C₂²×C₃	#120⋊C₃
prime radical	C₂×C₃×#997	C₂
LCS	G ▷ C₃×H(5,𝔽₂)
UCS	C₁ ◁ C₂²

384 conjugacy classes of subgroups; only the 31 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 31 normal subgroups are shown.

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

μ_t(G) = 96

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 155386);