C₅×C₁₃×C₃⋊D₅₁ #34091063

order	19890
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₁₃ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₅×C₁₃×C₃⋊D₅₁
unambiguous semidirect product	C₃⋊(C₅×C₁₃×D₅₁)
unambiguous semidirect product	C₁₇⋊(C₅×C₁₃×C₃⋊D₃)

	subgroup	G/H
center, hypercenter	C₅×C₁₃	C₃⋊D₅₁
commutator, cosocle, hypocenter	C₃²×C₁₇	C₂×C₅×C₁₃
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₁₃×C₁₇	C₂
LCS	G ▷ C₃²×C₁₇
UCS	C₁ ◁ C₅×C₁₃

96 conjugacy classes of subgroups.

μ_t(G) = 9945

5070 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19890, 48);