C₂×C₁₉×C₃⋊D₆₉ #30628651

order	15732
isoclinism	isoclinic class of C₃⋊D₆₉
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₉ · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₂×C₁₉×C₃⋊D₆₉
unambiguous semidirect product	(C₂×C₃)⋊(C₁₉×D₆₉)
unambiguous semidirect product	(C₂×C₂₃)⋊(C₃⋊D₃×C₁₉)

	subgroup	G/H
center, hypercenter	C₂×C₁₉	C₃⋊D₆₉
commutator, cosocle, hypocenter	C₃²×C₂₃	C₂²×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₁₉×C₂₃	C₂
LCS	G ▷ C₃²×C₂₃
UCS	C₁ ◁ C₂×C₁₉

120 conjugacy classes of subgroups.

μ_t(G) = 7866

3990 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15732, 113);