D₃×C₂²⋊(Q₈⋊C₉) #13164656

order	1728
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product	D₃×C₂²⋊(Q₈⋊C₉)
unambiguous semidirect product	C₃⋊(C₂×C₂²⋊(Q₈⋊C₉))

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₃	D₃×C₂²⋊A₄
commutator, hypocenter	C₂²×C₃×Q₈	C₂×C₉
Fitting, cosocle	C₂²×C₃²×Q₈	C₂×C₃
socle	C₂³×C₃²	C₂×A₄
prime radical	C₂³×C₃×D₃	A₄
LCS	G ▷ C₂²×C₃×Q₈
UCS	C₁ ◁ C₂×C₃

701 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 701 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.

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

μ_t(G) = 144

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 30719);