C₁₇×D₂₁×C₅₃ #49180918

order	37842
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₇×C₅₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₇×D₂₁×C₅₃
unambiguous semidirect product	C₃⋊(D₇×C₁₇×C₅₃)
unambiguous semidirect product	C₇⋊(D₃×C₁₇×C₅₃)

	subgroup	G/H
center, hypercenter	C₁₇×C₅₃	D₂₁
commutator, cosocle, hypocenter	C₃×C₇	C₂×C₁₇×C₅₃
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₇×C₅₃	C₂
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₁₇×C₅₃

32 conjugacy classes of subgroups.

μ_t(G) = 18921

10812 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37842, 14);