C₂×C₃×#5930 #11923747

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

Aliases

	subgroup	G/H
center, hypercenter	C₂²×C₃	#1020
commutator, cosocle, hypocenter	C₂²⋊SL(2,𝔽₃)	C₂²×C₃
Frattini	C₂	C₂×C₃×#1020
Fitting	C₂³×C₃×Q₈	D₃
socle	C₂⁴×C₃	S₄
prime radical	C₂×C₃×C₂²⋊SL(2,𝔽₃)	C₂
LCS	G ▷ C₂²⋊SL(2,𝔽₃)
UCS	C₁ ◁ C₂²×C₃

556 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.

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

μ_t(G) = 288

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 157758);