C₅×D₅×D₉×C₁₉ #30685589

order	17100
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₅×D₅×D₉×C₁₉
unambiguous semidirect product	(C₅×D₉)⋊(C₂×C₅×C₁₉)
unambiguous semidirect product	(C₉×D₅)⋊(C₂×C₅×C₁₉)
unambiguous semidirect product	D₄₅⋊(C₂×C₅×C₁₉)

	subgroup	G/H
center, hypercenter	C₅×C₁₉	D₅×D₉
commutator, cosocle, hypocenter	C₅×C₉	C₂²×C₅×C₁₉
Frattini	C₃	C₅×D₃×D₅×C₁₉
Fitting	C₅²×C₉×C₁₉	C₂²
socle	C₃×C₅²×C₁₉	C₂×D₃
LCS	G ▷ C₅×C₉
UCS	C₁ ◁ C₅×C₁₉

144 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.

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

μ_t(G) = 1710

2280 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 226);