C₂×C₇×C₁₉×D₃₉ #35209207

order	20748
automorphism	?
homology	Abelianization (H₁) = C₂²×C₇×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₇×C₁₉×D₃₉
unambiguous semidirect product	(C₂×C₃)⋊(C₇×C₁₉×D₁₃)
unambiguous semidirect product	(C₂×C₁₃)⋊(D₃×C₇×C₁₉)

	subgroup	G/H
center, hypercenter	C₂×C₇×C₁₉	D₃₉
commutator, cosocle, hypocenter	C₃×C₁₃	C₂²×C₇×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₇×C₁₃×C₁₉	C₂
LCS	G ▷ C₃×C₁₃
UCS	C₁ ◁ C₂×C₇×C₁₉

80 conjugacy classes of subgroups.

μ_t(G) = 10374

5586 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20748, 435);