D₃×D₅×A₄ #10624328

order	720
isoclinism	isoclinic class of D₃×D₅×A₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product	D₃×D₅×A₄
unambiguous semidirect product	(C₅×D₃)⋊(C₂×A₄)
unambiguous semidirect product	(C₃×D₅)⋊(C₂×A₄)
unambiguous semidirect product	D₁₅⋊(C₂×A₄)
unambiguous semidirect product	(C₂²×D₃×D₅)⋊C₃

Fitting, socle, derived	C₂²×C₃×C₅ ⋊ C₂²×C₃
Sylow	C₅ ⋊ C₂×D₃×A₄

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₂²×C₃×C₅	C₂²×C₃
LCS	G ▷ C₂²×C₃×C₅
UCS	C₁

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

normal subgroups only

This group has 164 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.

μ_t(G) = 60

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(720, 797);