C₇×D₁₉×D₁₃⋊C₃ #35208902

order	20748
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₇ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₇×D₁₉×D₁₃⋊C₃
unambiguous semidirect product	D₁₃⋊(C₃×C₇×D₁₉)
unambiguous semidirect product	(D₁₉×C₁₃⋊C₃)⋊(C₂×C₇)
unambiguous semidirect product	(C₁₉×D₁₃⋊C₃)⋊(C₂×C₇)
unambiguous semidirect product	((C₁₃⋊C₃)⋊D₁₉)⋊(C₂×C₇)

	subgroup	G/H
center, hypercenter	C₇	D₁₉×D₁₃⋊C₃
commutator, cosocle, hypocenter	C₁₃×C₁₉	C₂²×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₇×C₁₃×C₁₉	C₂²×C₃
LCS	G ▷ C₁₃×C₁₉
UCS	C₁ ◁ C₇

80 conjugacy classes of subgroups.

μ_t(G) = 1729

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20748, 130);