C₂×D₅×C₃₁×C₁₉⋊C₃ #47977705

order	35340
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₃₁ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×D₅×C₃₁×C₁₉⋊C₃
unambiguous semidirect product	C₅⋊(C₂²×C₃₁×C₁₉⋊C₃)
unambiguous semidirect product	(C₂×C₅)⋊(C₂×C₃₁×C₁₉⋊C₃)
unambiguous semidirect product	(C₂×D₅×C₁₉)⋊(C₃×C₃₁)

	subgroup	G/H
center, hypercenter	C₂×C₃₁	D₅×C₁₉⋊C₃
commutator, cosocle, hypocenter	C₅×C₁₉	C₂²×C₃×C₃₁
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₉×C₃₁	C₂×C₃
LCS	G ▷ C₅×C₁₉
UCS	C₁ ◁ C₂×C₃₁

80 conjugacy classes of subgroups.

μ_t(G) = 5890

2232 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35340, 177);