C₂×C₅⋊(#392⋊C₃) #14512082

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product	C₂×C₅⋊(#392⋊C₃)
unambiguous semidirect product	(C₂×C₅)⋊(#392⋊C₃)
unambiguous semidirect product	(C₂×#64960)⋊C₃

Hall	C₂×#64960 ⋊ C₃
Sylow	C₅ ⋊ C₂×#392⋊C₃

	subgroup	G/H
center, hypercenter	C₂²	C₅⋊(#127⋊C₃)
commutator, cosocle, hypocenter	C₅×#95	C₂²×C₃
Frattini	C₂³	C₂×D₅×A₄
Fitting	C₂×C₅×#95	C₂×C₃
socle	C₂⁴×C₅	C₂×A₄
LCS	G ▷ C₅×#95
UCS	C₁ ◁ C₂²

674 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 674 conjugacy classes of subgroups — too many to draw. Only its 37 normal subgroups are shown.

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

μ_t(G) = 120

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 237780);