C₃×C₇×C₁₉×C₃₁⋊C₃ #49150809

order	37107
automorphism	?
homology	Abelianization (H₁) = C₃²×C₇×C₁₉ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃×C₇×C₁₉×C₃₁⋊C₃
unambiguous semidirect product	C₃₁⋊(C₃²×C₇×C₁₉)
unambiguous semidirect product	(C₃×C₃₁)⋊(C₃×C₇×C₁₉)

	subgroup	G/H
center, hypercenter	C₃×C₇×C₁₉	C₃₁⋊C₃
commutator, cosocle, hypocenter	C₃₁	C₃²×C₇×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₉×C₃₁	C₃
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₃×C₇×C₁₉

48 conjugacy classes of subgroups.

μ_t(G) = 12369

5187 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37107, 38);