C₂×C₃×C₇×C₁₉×D₂₃ #49144841

order	36708
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₇×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₃×C₇×C₁₉×D₂₃
unambiguous semidirect product	C₂₃⋊(C₂²×C₃×C₇×C₁₉)
unambiguous semidirect product	(C₂×C₂₃)⋊(C₂×C₃×C₇×C₁₉)

	subgroup	G/H
center, hypercenter	C₂×C₃×C₇×C₁₉	D₂₃
commutator, cosocle, hypocenter	C₂₃	C₂²×C₃×C₇×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₇×C₁₉×C₂₃	C₂
LCS	G ▷ C₂₃
UCS	C₁ ◁ C₂×C₃×C₇×C₁₉

80 conjugacy classes of subgroups.

μ_t(G) = 18354

10374 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36708, 150);