C₃×C₅²×C₂²⋊(C₁₉⋊C₃) #30685960

order	17100
isoclinism	isoclinic class of C₂²⋊(C₁₉⋊C₃)
automorphism	?
homology	Abelianization (H₁) = C₃²×C₅² · Schur multiplier (H₂) = C₂×C₃×C₅

Aliases

direct product	C₃×C₅²×C₂²⋊(C₁₉⋊C₃)
unambiguous semidirect product	(C₂²×C₃)⋊(C₅²×C₁₉⋊C₃)
unambiguous semidirect product	(C₃×C₁₉)⋊(C₅²×A₄)
unambiguous semidirect product	(C₂²×C₃×C₅)⋊(C₅×C₁₉⋊C₃)
unambiguous semidirect product	(C₃×C₅×C₁₉)⋊(C₅×A₄)

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

224 conjugacy classes of subgroups.

μ_t(G) = 5700

2100 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 597);