D₇×C₁₉×D₁₃⋊C₃ #35209015

order	20748
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₇×C₁₉×D₁₃⋊C₃
unambiguous semidirect product	D₁₃⋊(C₃×D₇×C₁₉)
unambiguous semidirect product	(C₇×D₁₃⋊C₃)⋊(C₂×C₁₉)
unambiguous semidirect product	(D₇×C₁₃⋊C₃)⋊(C₂×C₁₉)
unambiguous semidirect product	((C₁₃⋊C₃)⋊D₇)⋊(C₂×C₁₉)

	subgroup	G/H
center, hypercenter	C₁₉	D₇×D₁₃⋊C₃
commutator, cosocle, hypocenter	C₇×C₁₃	C₂²×C₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₇×C₁₃×C₁₉	C₂²×C₃
LCS	G ▷ C₇×C₁₃
UCS	C₁ ◁ C₁₉

80 conjugacy classes of subgroups.

μ_t(G) = 1729

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20748, 243);