C₁₉×D₈₉₇ #46801769

order	34086
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₉×D₈₉₇
unambiguous semidirect product	C₃⋊(C₁₉×D₂₉₉)
unambiguous semidirect product	C₁₃⋊(C₁₉×D₆₉)
unambiguous semidirect product	C₂₃⋊(C₁₉×D₃₉)

	subgroup	G/H
center, hypercenter	C₁₉	D₈₉₇
commutator, cosocle, hypocenter	C₃×C₁₃×C₂₃	C₂×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₁₃×C₁₉×C₂₃	C₂
LCS	G ▷ C₃×C₁₃×C₂₃
UCS	C₁ ◁ C₁₉

32 conjugacy classes of subgroups.

μ_t(G) = 17043

8550 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34086, 18);