C₂×(C₃⋊D₃)⋊(C₄²⋊C₃) #13147197

order	1728
isoclinism	isoclinic class of (C₃⋊D₃)⋊(C₄²⋊C₃)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂×C₃×C₄

Aliases

direct product	C₂×(C₃⋊D₃)⋊(C₄²⋊C₃)
unambiguous semidirect product	(C₂×C₃⋊D₃)⋊(C₄²⋊C₃)

Fitting	C₂×C₃²×C₄² ⋊ C₂×C₃
derived	C₃²×C₄² ⋊ C₂²×C₃

	subgroup	G/H
center, hypercenter	C₂	(C₃⋊D₃)⋊(C₄²⋊C₃)
commutator, cosocle, hypocenter	C₃²×C₄²	C₂²×C₃
Frattini	C₂²×C₃	C₂×D₃×A₄
Fitting	C₂×C₃²×C₄²	C₂×C₃
socle	C₂³×C₃	D₃×A₄
LCS	G ▷ C₃²×C₄²
UCS	C₁ ◁ C₂

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

normal subgroups only

This group has 585 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) = 36

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 13260);