D₃×C₂₃×C₃⋊(C₅⋊D₅) #35208203

order	20700
automorphism	?
homology	Abelianization (H₁) = C₂²×C₂₃ · Schur multiplier (H₂) = C₂×C₅

Aliases

direct product	D₃×C₂₃×C₃⋊(C₅⋊D₅)
unambiguous semidirect product	(C₃×D₃)⋊(C₂₃×C₅⋊D₅)
unambiguous semidirect product	(C₅×D₃)⋊(C₂₃×D₁₅)

	subgroup	G/H
center, hypercenter	C₂₃	D₃×C₃⋊(C₅⋊D₅)
commutator, cosocle, hypocenter	C₃²×C₅²	C₂²×C₂₃
Frattini	C₁	G
Fitting, socle	C₃²×C₅²×C₂₃	C₂²
LCS	G ▷ C₃²×C₅²
UCS	C₁ ◁ C₂₃

352 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 104 normal subgroups are shown.

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

μ_t(G) = 3450

2691 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20700, 319);