D₁₅×C₄²⋊C₃ #13086234

order	1440
isoclinism	isoclinic class of D₁₅×C₄²⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₄

Aliases

direct product	D₁₅×C₄²⋊C₃
unambiguous semidirect product	C₃⋊(D₅×C₄²⋊C₃)
unambiguous semidirect product	C₅⋊(D₃×C₄²⋊C₃)
unambiguous semidirect product	(C₄²×D₁₅)⋊C₃

Fitting, derived	C₃×C₄²×C₅ ⋊ C₂×C₃
Sylow	C₅ ⋊ D₃×C₄²⋊C₃

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₃×C₄²×C₅	C₂×C₃
Frattini	C₂²	A₄×D₁₅
socle	C₂²×C₃×C₅	C₂×A₄
LCS	G ▷ C₃×C₄²×C₅
UCS	C₁

118 conjugacy classes of subgroups; only the 20 normal subgroups are shown.

normal subgroups only

This group has 118 conjugacy classes of subgroups — too many to draw. Only its 20 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, 2551);