C₃×C₁₉⋊C₃×C₁₇₉ #44499477

order	30609
automorphism	?
homology	Abelianization (H₁) = C₃²×C₁₇₉ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃×C₁₉⋊C₃×C₁₇₉
unambiguous semidirect product	C₁₉⋊(C₃²×C₁₇₉)
unambiguous semidirect product	(C₃×C₁₉)⋊(C₃×C₁₇₉)
unambiguous semidirect product	(C₁₉×C₁₇₉)⋊C₃²
unambiguous semidirect product	(C₃×C₁₉×C₁₇₉)⋊C₃

	subgroup	G/H
center, hypercenter	C₃×C₁₇₉	C₁₉⋊C₃
commutator, cosocle, hypocenter	C₁₉	C₃²×C₁₇₉
Frattini	C₁	G
Fitting, socle	C₃×C₁₉×C₁₇₉	C₃
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₃×C₁₇₉

24 conjugacy classes of subgroups.

μ_t(G) = 10203

4833 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30609, 5);