C₃×C₁₉⋊C₃×C₁₃₇ #37552844

order	23427
automorphism	?
homology	Abelianization (H₁) = C₃²×C₁₃₇ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃×C₁₉⋊C₃×C₁₃₇
unambiguous semidirect product	C₁₉⋊(C₃²×C₁₃₇)
unambiguous semidirect product	(C₃×C₁₉)⋊(C₃×C₁₃₇)
unambiguous semidirect product	(C₁₉×C₁₃₇)⋊C₃²
unambiguous semidirect product	(C₃×C₁₉×C₁₃₇)⋊C₃

	subgroup	G/H
center, hypercenter	C₃×C₁₃₇	C₁₉⋊C₃
commutator, cosocle, hypocenter	C₁₉	C₃²×C₁₃₇
Frattini	C₁	G
Fitting, socle	C₃×C₁₉×C₁₃₇	C₃
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₃×C₁₃₇

24 conjugacy classes of subgroups.

μ_t(G) = 7809

3699 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23427, 5);