C₂×C₃⋊D₃×C₄²⋊C₃ #13173138

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	C₂×A₄×C₃⋊D₃
Fitting	C₂×C₃²×C₄²	C₂×C₃
socle	C₂³×C₃²	C₂×A₄
LCS	G ▷ C₃²×C₄²
UCS	C₁ ◁ C₂

696 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 696 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.

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

μ_t(G) = 108

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 39201);