C₁₇×C₃⋊(C₅⋊(D₁₃⋊C₃)) #34091052

order	19890
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₇×C₃⋊(C₅⋊(D₁₃⋊C₃))
unambiguous semidirect product	C₃⋊(C₁₇×C₅⋊(D₁₃⋊C₃))
unambiguous semidirect product	C₅⋊(C₁₇×C₃⋊(D₁₃⋊C₃))
unambiguous semidirect product	(C₁₃⋊C₃)⋊(C₁₇×D₁₅)
unambiguous semidirect product	D₁₉₅⋊(C₃×C₁₇)
unambiguous semidirect product	(C₁₇×D₁₉₅)⋊C₃

	subgroup	G/H
center, hypercenter	C₁₇	C₃⋊(C₅⋊(D₁₃⋊C₃))
commutator, cosocle, hypocenter	C₃×C₅×C₁₃	C₂×C₃×C₁₇
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₃×C₁₇	C₂×C₃
LCS	G ▷ C₃×C₅×C₁₃
UCS	C₁ ◁ C₁₇

72 conjugacy classes of subgroups.

μ_t(G) = 3315

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19890, 37);