C₂×C₃×C₅×#226 #13089048

order	1440
isoclinism	isoclinic class of #226
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₅ · Schur multiplier (H₂) = C₂

Aliases

C₂×C₃×C₅×#226

	subgroup	G/H
center, socle, hypercenter	C₂²×C₃×C₅	S₄
commutator, cosocle, hypocenter	SL(2,𝔽₃)	C₂²×C₃×C₅
Frattini	C₂	C₂×C₃×C₅×S₄
Fitting	C₂×C₃×C₅×Q₈	D₃
prime radical	C₂×C₃×C₅×SL(2,𝔽₃)	C₂
LCS	G ▷ SL(2,𝔽₃)
UCS	C₁ ◁ C₂²×C₃×C₅

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

normal subgroups only

This group has 170 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) = 480

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 5365);