C₂×#63689⋊C₃ #13164409

order	1728
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product	C₂×#63689⋊C₃
unambiguous semidirect product	(C₂×#63689)⋊C₃

	subgroup	G/H
center	C₂²	C₂×((C₂²⋊C₉)⋊C₂)⋊C₃
commutator, cosocle, hypocenter	Q₈⋊C₉	C₂³×C₃
Frattini	C₂×C₃	C₂²×C₃×S₄
Fitting	C₂²×C₃²×Q₈	D₃
socle	C₂²×C₃	C₂×C₃×S₄
hypercenter	C₂³	((C₂²⋊C₉)⋊C₂)⋊C₃
LCS	G ▷ Q₈⋊C₉
UCS	C₁ ◁ C₂² ◁ C₂³

566 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.

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

μ_t(G) = 288

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 30472);