C₂×C₃×C₇×C₁₃×C₁₉⋊C₃ #44528010

order	31122
automorphism	?
homology	Abelianization (H₁) = C₂×C₃²×C₇×C₁₃ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₂×C₃×C₇×C₁₃×C₁₉⋊C₃
unambiguous semidirect product	(C₂×C₁₉)⋊(C₃²×C₇×C₁₃)
unambiguous semidirect product	(C₂×C₃×C₁₉)⋊(C₃×C₇×C₁₃)

	subgroup	G/H
center, hypercenter	C₂×C₃×C₇×C₁₃	C₁₉⋊C₃
commutator, cosocle, hypocenter	C₁₉	C₂×C₃²×C₇×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₇×C₁₃×C₁₉	C₃
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂×C₃×C₇×C₁₃

96 conjugacy classes of subgroups.

μ_t(G) = 10374

4914 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31122, 493);