C₅×D₃×C₂²⋊A₄ #13089620

order	1440
isoclinism	isoclinic class of D₃×C₂²⋊A₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₅ · Schur multiplier (H₂) = C₂⁴

Aliases

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

Fitting, socle	C₂⁴×C₃×C₅ ⋊ C₂×C₃
derived	C₂⁴×C₃ ⋊ C₂×C₃×C₅

	subgroup	G/H
center, hypercenter	C₅	D₃×C₂²⋊A₄
commutator, cosocle, hypocenter	C₂⁴×C₃	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₂⁴×C₃×C₅	C₂×C₃
LCS	G ▷ C₂⁴×C₃
UCS	C₁ ◁ C₅

606 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 606 conjugacy classes of subgroups — too many to draw. Only its 48 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, 5937);