C₂×(((C₃⋊D₃)⋊C₉)⋊C₂)⋊C₃ #14518290

order	1944
isoclinism	isoclinic class of (((C₃⋊D₃)⋊C₉)⋊C₂)⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product	C₂×(((C₃⋊D₃)⋊C₉)⋊C₂)⋊C₃
unambiguous semidirect product	(((C₃⋊D₃)⋊C₉)⋊C₂)⋊(C₂×C₃)
unambiguous semidirect product	#92259⋊C₂²
unambiguous semidirect product	(#4169⋊C₃)⋊C₂²
unambiguous semidirect product	#92302⋊C₂²
unambiguous semidirect product	(C₂×((C₃⋊D₃)⋊C₉)⋊C₂)⋊C₃

	subgroup	G/H
center, hypercenter	C₂	(((C₃⋊D₃)⋊C₉)⋊C₂)⋊C₃
commutator, cosocle, hypocenter	C₃²⋊C₉	C₂³×C₃
Frattini	C₃²	C₂×C₃×D₃²
Fitting	C₂×#6891	C₂²
socle	C₂×C₃²	C₃×D₃²
LCS	G ▷ C₃²⋊C₉
UCS	C₁ ◁ C₂

532 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 69 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(1944, 2684);