C₂×C₃×D₃×C₁₉×C₅₃ #49136335

order	36252
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₁₉×C₅₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₃×D₃×C₁₉×C₅₃
unambiguous semidirect product	C₃⋊(C₂²×C₃×C₁₉×C₅₃)
unambiguous semidirect product	(C₂×C₃)⋊(C₂×C₃×C₁₉×C₅₃)

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₉×C₅₃	D₃
commutator, cosocle, hypocenter	C₃	C₂²×C₃×C₁₉×C₅₃
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₁₉×C₅₃	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₁₉×C₅₃

88 conjugacy classes of subgroups.

μ_t(G) = 12084

18126 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36252, 134);