C₃×C₅×((C₃⋊D₃)⋊C₃)⋊C₂ #13108409

order	1620
isoclinism	isoclinic class of ((C₃⋊D₃)⋊C₃)⋊C₂
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₅ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₃×C₅×((C₃⋊D₃)⋊C₃)⋊C₂
unambiguous semidirect product	((C₃⋊D₃)⋊C₃)⋊(C₂×C₃×C₅)

	subgroup	G/H
center, hypercenter	C₃×C₅	((C₃⋊D₃)⋊C₃)⋊C₂
commutator, cosocle, hypocenter	H(3,𝔽₃)	C₂²×C₃×C₅
Frattini	C₃	C₃×C₅×D₃²
Fitting	C₃×C₅×H(3,𝔽₃)	C₂²
socle	C₃²×C₅	D₃²
LCS	G ▷ H(3,𝔽₃)
UCS	C₁ ◁ C₃×C₅

206 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.

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

μ_t(G) = 90

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1620, 315);