C₂²×C₃×#984 #11923695

order	1152
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃ · Schur multiplier (H₂) = C₂⁶

Aliases

C₂²×C₃×#984

	subgroup	G/H
center, socle	C₂³×C₃	C₂×S₄
commutator, cosocle, hypocenter	SL(2,𝔽₃)	C₂⁴×C₃
Frattini	C₂	C₂³×C₃×S₄
Fitting	C₂²×C₃×#41	D₃
prime radical	C₂²×C₃×#41⋊C₃	C₂
hypercenter	C₂²×C₃×C₄	S₄
LCS	G ▷ SL(2,𝔽₃)
UCS	C₁ ◁ C₂³×C₃ ◁ C₂²×C₃×C₄

1529 conjugacy classes of subgroups; only the 220 normal subgroups are shown.

normal subgroups only

This group has 1529 conjugacy classes of subgroups — too many to draw. Only its 220 normal subgroups are shown.

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

μ_t(G) = 384

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 157706);