C₅×D₃×C₃₆₁⋊C₃ #44570437

order	32490
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₅ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×D₃×C₃₆₁⋊C₃
unambiguous semidirect product	C₃⋊(C₂×C₅×C₃₆₁⋊C₃)
unambiguous semidirect product	(D₃×C₃₆₁)⋊(C₃×C₅)
unambiguous semidirect product	(C₅×D₃×C₃₆₁)⋊C₃

	subgroup	G/H
center, hypercenter	C₅	D₃×C₃₆₁⋊C₃
commutator, cosocle, hypocenter	C₃×C₃₆₁	C₂×C₃×C₅
Frattini	C₁₉	C₅×D₃×C₁₉⋊C₃
Fitting	C₃×C₅×C₃₆₁	C₂×C₃
socle	C₃×C₅×C₁₉	C₂×C₁₉⋊C₃
LCS	G ▷ C₃×C₃₆₁
UCS	C₁ ◁ C₅

54 conjugacy classes of subgroups.

μ_t(G) = 5415

1845 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32490, 21);