D₃×D₅×SL(2,𝔽₃) #13088598

order	1440
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₃×D₅×SL(2,𝔽₃)
unambiguous semidirect product	(C₅×D₃)⋊(C₂×SL(2,𝔽₃))
unambiguous semidirect product	(C₃×D₅)⋊(C₂×SL(2,𝔽₃))
unambiguous semidirect product	D₁₅⋊(C₂×SL(2,𝔽₃))
unambiguous semidirect product	(D₃×Q₈×D₅)⋊C₃

Fitting, derived	C₃×C₅×Q₈ ⋊ C₂²×C₃
Sylow	C₅ ⋊ C₂×D₃×SL(2,𝔽₃)

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃×D₅×A₄
commutator, Fitting, cosocle, hypocenter	C₃×C₅×Q₈	C₂²×C₃
socle	C₂×C₃×C₅	C₂²×A₄
LCS	G ▷ C₃×C₅×Q₈
UCS	C₁ ◁ C₂

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

normal subgroups only

This group has 258 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) = 120

maximal subgroup of	D₃×D₅×#997, D₃×AGL(1,𝔽₅)×SL(2,𝔽₃), D₃×D₅×GL(2,𝔽₃), …
maximal normal subgroup of	D₃×AGL(1,𝔽₅)×SL(2,𝔽₃), D₃×D₅×GL(2,𝔽₃), D₃×#91886

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 4915);