C₂×C₅₃×D₁₇₁ #49136236

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

Aliases

direct product	C₂×C₅₃×D₁₇₁
unambiguous semidirect product	(C₂×C₉)⋊(D₁₉×C₅₃)
unambiguous semidirect product	(C₂×C₁₉)⋊(D₉×C₅₃)

	subgroup	G/H
center, hypercenter	C₂×C₅₃	D₁₇₁
commutator, cosocle, hypocenter	C₉×C₁₉	C₂²×C₅₃
Frattini	C₃	C₂×C₅₃×D₅₇
Fitting	C₂×C₉×C₁₉×C₅₃	C₂
socle	C₂×C₃×C₁₉×C₅₃	D₃
LCS	G ▷ C₉×C₁₉
UCS	C₁ ◁ C₂×C₅₃

60 conjugacy classes of subgroups.

μ_t(G) = 18126

9222 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36252, 35);