D₃×#396⋊C₃ #11921186

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

Aliases

direct product	D₃×#396⋊C₃
unambiguous semidirect product	(D₃×#396)⋊C₃

Fitting	C₃×#396 ⋊ C₂×C₃
derived	C₃×#95 ⋊ C₂²×C₃

	subgroup	G/H
center, hypercenter	C₂	D₃×#126⋊C₃
commutator, cosocle, hypocenter	C₃×#95	C₂²×C₃
Frattini	C₂³	C₂×D₃×A₄
Fitting	C₃×#396	C₂×C₃
socle	C₂³×C₃	C₂²×A₄
LCS	G ▷ C₃×#95
UCS	C₁ ◁ C₂

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

normal subgroups only

This group has 438 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) = 36

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 155197);