C₂×C₃×C₁₉×D₁₃₇ #44530346

order	31236
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₃×C₁₉×D₁₃₇
unambiguous semidirect product	C₁₃₇⋊(C₂²×C₃×C₁₉)
unambiguous semidirect product	(C₂×C₁₃₇)⋊(C₂×C₃×C₁₉)

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₉	D₁₃₇
commutator, cosocle, hypocenter	C₁₃₇	C₂²×C₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₉×C₁₃₇	C₂
LCS	G ▷ C₁₃₇
UCS	C₁ ◁ C₂×C₃×C₁₉

40 conjugacy classes of subgroups.

μ_t(G) = 15618

7980 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31236, 34);