C₇×C₅₃×D₅₁ #49180916

order	37842
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₅₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×C₅₃×D₅₁
unambiguous semidirect product	C₃⋊(C₇×D₁₇×C₅₃)
unambiguous semidirect product	C₁₇⋊(D₃×C₇×C₅₃)

	subgroup	G/H
center, hypercenter	C₇×C₅₃	D₅₁
commutator, cosocle, hypocenter	C₃×C₁₇	C₂×C₇×C₅₃
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₇×C₅₃	C₂
LCS	G ▷ C₃×C₁₇
UCS	C₁ ◁ C₇×C₅₃

32 conjugacy classes of subgroups.

μ_t(G) = 18921

10017 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37842, 12);