C₂×C₃×C₁₉⋊C₃×C₈₉ #44478447

order	30438
automorphism	?
homology	Abelianization (H₁) = C₂×C₃²×C₈₉ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₂×C₃×C₁₉⋊C₃×C₈₉
unambiguous semidirect product	(C₂×C₁₉)⋊(C₃²×C₈₉)
unambiguous semidirect product	(C₂×C₃×C₁₉)⋊(C₃×C₈₉)
unambiguous semidirect product	(C₂×C₁₉×C₈₉)⋊C₃²
unambiguous semidirect product	(C₂×C₃×C₁₉×C₈₉)⋊C₃

	subgroup	G/H
center, hypercenter	C₂×C₃×C₈₉	C₁₉⋊C₃
commutator, cosocle, hypocenter	C₁₉	C₂×C₃²×C₈₉
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₉×C₈₉	C₃
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂×C₃×C₈₉

48 conjugacy classes of subgroups.

μ_t(G) = 10146

4806 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30438, 25);