C₂×C₁₉×D₁₃₉⋊C₃ #44540092

order	31692
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₁₉×D₁₃₉⋊C₃
unambiguous semidirect product	D₁₃₉⋊(C₂×C₃×C₁₉)
unambiguous semidirect product	(C₁₃₉⋊C₃)⋊(C₂²×C₁₉)
unambiguous semidirect product	(C₂×D₁₃₉)⋊(C₃×C₁₉)
unambiguous semidirect product	(C₂×C₁₃₉⋊C₃)⋊(C₂×C₁₉)

	subgroup	G/H
center, hypercenter	C₂×C₁₉	D₁₃₉⋊C₃
commutator, cosocle, hypocenter	C₁₃₉	C₂²×C₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₁₉×C₁₃₉	C₂×C₃
LCS	G ▷ C₁₃₉
UCS	C₁ ◁ C₂×C₁₉

40 conjugacy classes of subgroups.

μ_t(G) = 5282

1102 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31692, 30);