C₂×C₅×C₁₉×ΓL(1,𝔽₃₂) #44441303

order	29450
automorphism	?
homology	Abelianization (H₁) = C₂×C₅²×C₁₉ · Schur multiplier (H₂) = C₅

Aliases

direct product	C₂×C₅×C₁₉×ΓL(1,𝔽₃₂)
unambiguous semidirect product	(C₂×C₃₁)⋊(C₅²×C₁₉)
unambiguous semidirect product	(C₂×C₅×C₃₁)⋊(C₅×C₁₉)
unambiguous semidirect product	(C₂×C₁₉×C₃₁)⋊C₅²
unambiguous semidirect product	(C₂×C₅×C₁₉×C₃₁)⋊C₅

	subgroup	G/H
center, hypercenter	C₂×C₅×C₁₉	ΓL(1,𝔽₃₂)
commutator, cosocle, hypocenter	C₃₁	C₂×C₅²×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₉×C₃₁	C₅
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₂×C₅×C₁₉

64 conjugacy classes of subgroups.

μ_t(G) = 5890

2090 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29450, 21);