C₂×C₅⋊#5930 #14514623

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂³

Aliases

direct product	C₂×C₅⋊#5930
unambiguous semidirect product	(C₂×C₅)⋊#5930

	subgroup	G/H
center, hypercenter	C₂²	C₅⋊#1020
commutator, cosocle, hypocenter	C₅×C₂²⋊SL(2,𝔽₃)	C₂²
Frattini	C₂	C₂×C₅⋊#1020
Fitting	C₂³×C₅×Q₈	D₃
socle	C₂⁴×C₅	S₄
prime radical	C₂×C₅×C₂²⋊SL(2,𝔽₃)	C₂
LCS	G ▷ C₅×C₂²⋊SL(2,𝔽₃)
UCS	C₁ ◁ C₂²

536 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.

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

μ_t(G) = 480

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240321);