C₂²×#91954 #14514602

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁶

Aliases

	subgroup	G/H
center	C₂³	C₂×C₅⋊S₄
commutator, cosocle, hypocenter	C₅×SL(2,𝔽₃)	C₂⁴
Frattini	C₂	C₂³×C₅⋊S₄
Fitting	C₂²×C₅×#41	D₃
socle	C₂³×C₅	C₂×S₄
prime radical	C₂²×C₅×#41⋊C₃	C₂
hypercenter	C₂²×C₄	C₅⋊S₄
LCS	G ▷ C₅×SL(2,𝔽₃)
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄

1486 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 1486 conjugacy classes of subgroups — too many to draw. Only its 169 normal subgroups are shown.

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

μ_t(G) = 640

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240300);