C₂×C₅×C₁₉⋊C₃×D₂₉ #45683283

order	33060
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₅ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₅×C₁₉⋊C₃×D₂₉
unambiguous semidirect product	C₂₉⋊(C₂²×C₅×C₁₉⋊C₃)
unambiguous semidirect product	(C₂×C₂₉)⋊(C₂×C₅×C₁₉⋊C₃)
unambiguous semidirect product	(C₂×C₁₉×D₂₉)⋊(C₃×C₅)
unambiguous semidirect product	(C₂×C₅×C₁₉×D₂₉)⋊C₃

	subgroup	G/H
center, hypercenter	C₂×C₅	C₁₉⋊C₃×D₂₉
commutator, cosocle, hypocenter	C₁₉×C₂₉	C₂²×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₉×C₂₉	C₂×C₃
LCS	G ▷ C₁₉×C₂₉
UCS	C₁ ◁ C₂×C₅

80 conjugacy classes of subgroups.

μ_t(G) = 5510

1440 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33060, 47);