C₂×D₉×C₁₉×C₅₃ #49136238

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

Aliases

direct product	C₂×D₉×C₁₉×C₅₃
unambiguous semidirect product	C₉⋊(C₂²×C₁₉×C₅₃)
unambiguous semidirect product	(C₂×C₉)⋊(C₂×C₁₉×C₅₃)

	subgroup	G/H
center, hypercenter	C₂×C₁₉×C₅₃	D₉
commutator, cosocle, hypocenter	C₉	C₂²×C₁₉×C₅₃
Frattini	C₃	C₂×D₃×C₁₉×C₅₃
Fitting	C₂×C₉×C₁₉×C₅₃	C₂
socle	C₂×C₃×C₁₉×C₅₃	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₂×C₁₉×C₅₃

60 conjugacy classes of subgroups.

μ_t(G) = 18126

12084 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36252, 37);