C₂×C₅⋊(C₁₇⋊(D₁₉⋊C₃)) #34084338

order	19380
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₅⋊(C₁₇⋊(D₁₉⋊C₃))
unambiguous semidirect product	(C₂×C₅)⋊(C₁₇⋊(D₁₉⋊C₃))
unambiguous semidirect product	(C₂×C₁₇)⋊(C₅⋊(D₁₉⋊C₃))
unambiguous semidirect product	(C₂×C₁₉⋊C₃)⋊D₈₅
unambiguous semidirect product	(C₂×D₁₆₁₅)⋊C₃

	subgroup	G/H
center, hypercenter	C₂	C₅⋊(C₁₇⋊(D₁₉⋊C₃))
commutator, cosocle, hypocenter	C₅×C₁₇×C₁₉	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₇×C₁₉	C₂×C₃
LCS	G ▷ C₅×C₁₇×C₁₉
UCS	C₁ ◁ C₂

80 conjugacy classes of subgroups.

μ_t(G) = 3230

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19380, 50);