D₅×C₁₉⋊C₃×C₅₉ #46777528

order	33630
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₅₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₅×C₁₉⋊C₃×C₅₉
unambiguous semidirect product	C₅⋊(C₂×C₁₉⋊C₃×C₅₉)
unambiguous semidirect product	(D₅×C₁₉)⋊(C₃×C₅₉)
unambiguous semidirect product	(D₅×C₁₉×C₅₉)⋊C₃

	subgroup	G/H
center, hypercenter	C₅₉	D₅×C₁₉⋊C₃
commutator, cosocle, hypocenter	C₅×C₁₉	C₂×C₃×C₅₉
Frattini	C₁	G
Fitting, socle	C₅×C₁₉×C₅₉	C₂×C₃
LCS	G ▷ C₅×C₁₉
UCS	C₁ ◁ C₅₉

32 conjugacy classes of subgroups.

μ_t(G) = 5605

2124 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33630, 21);