C₂×C₃²×C₅×D₅×C₁₉ #30685980

order	17100
isoclinism	isoclinic class of D₅
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃²×C₅×C₁₉ · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₂×C₃²×C₅×D₅×C₁₉
unambiguous semidirect product	C₅⋊(C₂²×C₃²×C₅×C₁₉)
unambiguous semidirect product	(C₂×C₅)⋊(C₂×C₃²×C₅×C₁₉)

	subgroup	G/H
center, hypercenter	C₂×C₃²×C₅×C₁₉	D₅
commutator, cosocle, hypocenter	C₅	C₂²×C₃²×C₅×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅²×C₁₉	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₃²×C₅×C₁₉

288 conjugacy classes of subgroups; only the 168 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 168 normal subgroups are shown.

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

μ_t(G) = 3420

6840 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 617);