C₃×#87508 #11923750

order	1152
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂³

Aliases

	subgroup	G/H
center	C₂×C₃	C₂×#1020
commutator, cosocle, hypocenter	C₂²⋊SL(2,𝔽₃)	C₂²×C₃
Frattini	C₂	C₂×C₃×#1020
Fitting	C₂²×C₃×#41	D₃
socle	C₂³×C₃	C₂×S₄
prime radical	C₃×#5948	C₂
hypercenter	C₃×C₄	#1020
LCS	G ▷ C₂²⋊SL(2,𝔽₃)
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄

542 conjugacy classes of subgroups; only the 34 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 34 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, 157761);