C₂×C₃⋊D₃×C₁₉×C₂₃ #30628652

order	15732
isoclinism	isoclinic class of C₃⋊D₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₉×C₂₃ · Schur multiplier (H₂) = C₂×C₃

Aliases

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

	subgroup	G/H
center, hypercenter	C₂×C₁₉×C₂₃	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂²×C₁₉×C₂₃
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₁₉×C₂₃	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂×C₁₉×C₂₃

120 conjugacy classes of subgroups.

μ_t(G) = 7866

5244 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15732, 114);