C₅×D₃×C₄²⋊C₃ #13086227

order	1440
isoclinism	isoclinic class of D₃×C₄²⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₅ · Schur multiplier (H₂) = C₄

Aliases

direct product	C₅×D₃×C₄²⋊C₃
unambiguous semidirect product	C₃⋊(C₂×C₅×C₄²⋊C₃)
unambiguous semidirect product	(C₄²×D₃)⋊(C₃×C₅)
unambiguous semidirect product	(C₄²×C₅×D₃)⋊C₃

Fitting	C₃×C₄²×C₅ ⋊ C₂×C₃
derived	C₃×C₄² ⋊ C₂×C₃×C₅

	subgroup	G/H
center, hypercenter	C₅	D₃×C₄²⋊C₃
commutator, cosocle, hypocenter	C₃×C₄²	C₂×C₃×C₅
Frattini	C₂²	C₅×D₃×A₄
Fitting	C₃×C₄²×C₅	C₂×C₃
socle	C₂²×C₃×C₅	C₂×A₄
LCS	G ▷ C₃×C₄²
UCS	C₁ ◁ C₅

118 conjugacy classes of subgroups; only the 24 normal subgroups are shown.

normal subgroups only

This group has 118 conjugacy classes of subgroups — too many to draw. Only its 24 normal subgroups are shown.

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

μ_t(G) = 180

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 2544);