C₃×Q₈⋊(Q₈⋊C₉) #13152259

order	1728
automorphism	?
homology	Abelianization (H₁) = C₃×C₉ · Schur multiplier (H₂) = C₂²×C₃

Aliases

direct product	C₃×Q₈⋊(Q₈⋊C₉)
unambiguous semidirect product	(C₃×Q₈)⋊(Q₈⋊C₉)

Q₈² ⋊ C₃×C₉

	subgroup	G/H
center, socle, prime radical, hypercenter	C₂²×C₃²	C₂²⋊A₄
commutator, hypocenter	Q₈²	C₃×C₉
Frattini	C₂²×C₃	C₃×C₂²⋊A₄
Fitting	C₃²×Q₈²	C₃
cosocle	C₃×Q₈²	C₃²
LCS	G ▷ Q₈²
UCS	C₁ ◁ C₂²×C₃²

340 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.

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

μ_t(G) = 1728

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 18322);