C₁₉×D₁₁×D₁₃⋊C₃ #45656722

order	32604
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₁₉×D₁₁×D₁₃⋊C₃
unambiguous semidirect product	D₁₃⋊(C₃×C₁₉×D₁₁)
unambiguous semidirect product	(D₁₁×D₁₃)⋊(C₃×C₁₉)
unambiguous semidirect product	(C₁₁×D₁₃⋊C₃)⋊(C₂×C₁₉)
unambiguous semidirect product	(D₁₁×C₁₃⋊C₃)⋊(C₂×C₁₉)
unambiguous semidirect product	(C₁₁⋊(D₁₃⋊C₃))⋊(C₂×C₁₉)

	subgroup	G/H
center, hypercenter	C₁₉	D₁₁×D₁₃⋊C₃
commutator, cosocle, hypocenter	C₁₁×C₁₃	C₂²×C₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₁₁×C₁₃×C₁₉	C₂²×C₃
LCS	G ▷ C₁₁×C₁₃
UCS	C₁ ◁ C₁₉

80 conjugacy classes of subgroups.

μ_t(G) = 2717

1064 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32604, 72);