C₂×C₃×C₅⋊#226 #13089059

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

Aliases

direct product	C₂×C₃×C₅⋊#226
unambiguous semidirect product	(C₂×C₅)⋊(C₃×#226)

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

170 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 42 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, 5376);