D₃×C₃⋊#1042 #14268440

order	1800
isoclinism	isoclinic class of D₃×C₃⋊#1042
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₃×C₃⋊#1042
unambiguous semidirect product	(C₃×D₃)⋊#1042

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₅²	C₂×C₄
prime radical	C₃×C₅×D₃×D₅	C₂
cosocle	C₃²×C₅×D₅	C₂²
LCS	G ▷ C₃²×C₅²
UCS	C₁

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

normal subgroups only

This group has 149 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.

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 120

maximal subgroup of	D₃×D₅×ΓL(1,𝔽₁₆), D₃×AGL(1,𝔽₅)×D₁₅, D₃²×#1042
maximal normal subgroup of	D₃×D₅×ΓL(1,𝔽₁₆), D₃×AGL(1,𝔽₅)×D₁₅, D₃²×#1042

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1800, 634);