C₂×D₅×C₁₇×C₁₉⋊C₃ #34084337

order	19380
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×D₅×C₁₇×C₁₉⋊C₃
unambiguous semidirect product	C₅⋊(C₂²×C₁₇×C₁₉⋊C₃)
unambiguous semidirect product	(C₂×C₅)⋊(C₂×C₁₇×C₁₉⋊C₃)
unambiguous semidirect product	(C₂×D₅×C₁₉)⋊(C₃×C₁₇)
unambiguous semidirect product	(C₂×D₅×C₁₇×C₁₉)⋊C₃

	subgroup	G/H
center, hypercenter	C₂×C₁₇	D₅×C₁₉⋊C₃
commutator, cosocle, hypocenter	C₅×C₁₉	C₂²×C₃×C₁₇
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₇×C₁₉	C₂×C₃
LCS	G ▷ C₅×C₁₉
UCS	C₁ ◁ C₂×C₁₇

80 conjugacy classes of subgroups.

μ_t(G) = 3230

1224 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19380, 49);