S₄×AGL(1,ℤ/9) #13049202

order	1296
isoclinism	isoclinic class of S₄×AGL(1,ℤ/9)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product	S₄×AGL(1,ℤ/9)
unambiguous semidirect product	D₉⋊(C₃×S₄)
unambiguous semidirect product	(D₉×S₄)⋊C₃
unambiguous semidirect product	(S₄×3₋¹⁺²)⋊C₂
unambiguous semidirect product	(A₄⋊AGL(1,ℤ/9))⋊C₂
unambiguous semidirect product	(A₄×AGL(1,ℤ/9))⋊C₂

Fitting	C₂²×3₋¹⁺² ⋊ C₂×D₃
derived	C₉×A₄ ⋊ C₂²×C₃

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₉×A₄	C₂²×C₃
Frattini	C₃	C₃×D₃×S₄
Fitting	C₂²×3₋¹⁺²	C₂×D₃
socle	C₂²×C₃	C₃×D₃²
LCS	G ▷ C₉×A₄
UCS	C₁

241 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 241 conjugacy classes of subgroups — too many to draw. Only its 30 normal subgroups are shown.

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

minimal degree	μ(G) = 13
transitive degree	μ_t(G) = 36

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1296, 2920);