C₂×C₃×C₁₉×D₁₄₉ #46800823

order	33972
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₃×C₁₉×D₁₄₉
unambiguous semidirect product	C₁₄₉⋊(C₂²×C₃×C₁₉)
unambiguous semidirect product	(C₂×C₁₄₉)⋊(C₂×C₃×C₁₉)

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₉	D₁₄₉
commutator, cosocle, hypocenter	C₁₄₉	C₂²×C₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₉×C₁₄₉	C₂
LCS	G ▷ C₁₄₉
UCS	C₁ ◁ C₂×C₃×C₁₉

40 conjugacy classes of subgroups.

μ_t(G) = 16986

8664 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33972, 34);