C₃×#72986 #11920764

order	1152
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂

Aliases

	subgroup	G/H
center	C₂×C₃	C₂×#857
commutator, cosocle, hypocenter	#95⋊C₃	C₂²×C₃
Frattini	C₂³	C₂×C₃×S₄
Fitting	C₃×#376	D₃
socle	C₂³×C₃	C₂×S₄
prime radical	C₃×#95⋊C₃	C₂²
hypercenter	C₃×C₄	#857
LCS	G ▷ #95⋊C₃
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄

216 conjugacy classes of subgroups; only the 26 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 26 normal subgroups are shown.

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

μ_t(G) = 144

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 154775);