C₂×C₃×C₅²×D₃×C₁₉ #30685976

order	17100
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₅²×C₁₉ · Schur multiplier (H₂) = C₂×C₅

Aliases

direct product	C₂×C₃×C₅²×D₃×C₁₉
unambiguous semidirect product	C₃⋊(C₂²×C₃×C₅²×C₁₉)
unambiguous semidirect product	(C₂×C₃)⋊(C₂×C₃×C₅²×C₁₉)

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅²×C₁₉	D₃
commutator, cosocle, hypocenter	C₃	C₂²×C₃×C₅²×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅²×C₁₉	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₅²×C₁₉

352 conjugacy classes of subgroups; only the 224 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 224 normal subgroups are shown.

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

μ_t(G) = 5700

8550 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 613);