C₂²×C₅×#984 #14511418

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₅ · Schur multiplier (H₂) = C₂⁶

Aliases

C₂²×C₅×#984

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

1486 conjugacy classes of subgroups; only the 220 normal subgroups are shown.

normal subgroups only

This group has 1486 conjugacy classes of subgroups — too many to draw. Only its 220 normal subgroups are shown.

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

μ_t(G) = 640

260 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 237116);