C₂×C₃²×((C₃⋊D₃)⋊C₃)⋊C₂ #14519298

order	1944
isoclinism	isoclinic class of ((C₃⋊D₃)⋊C₃)⋊C₂
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃² · Schur multiplier (H₂) = C₂³×C₃

Aliases

direct product	C₂×C₃²×((C₃⋊D₃)⋊C₃)⋊C₂
unambiguous semidirect product	((C₃⋊D₃)⋊C₃)⋊(C₂²×C₃²)

	subgroup	G/H
center, hypercenter	C₂×C₃²	((C₃⋊D₃)⋊C₃)⋊C₂
commutator, cosocle, hypocenter	H(3,𝔽₃)	C₂³×C₃²
Frattini	C₃	C₂×C₃²×D₃²
Fitting	C₂×C₃²×H(3,𝔽₃)	C₂²
socle	C₂×C₃³	D₃²
LCS	G ▷ H(3,𝔽₃)
UCS	C₁ ◁ C₂×C₃²

1276 conjugacy classes of subgroups; only the 180 normal subgroups are shown.

normal subgroups only

This group has 1276 conjugacy classes of subgroups — too many to draw. Only its 180 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(1944, 3692);