C₂×C₁₉×D₇₉⋊C₃ #31824718

order	18012
isoclinism	isoclinic class of D₇₉⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₁₉×D₇₉⋊C₃
unambiguous semidirect product	D₇₉⋊(C₂×C₃×C₁₉)
unambiguous semidirect product	(C₇₉⋊C₃)⋊(C₂²×C₁₉)
unambiguous semidirect product	(C₂×D₇₉)⋊(C₃×C₁₉)
unambiguous semidirect product	(C₂×C₇₉⋊C₃)⋊(C₂×C₁₉)

	subgroup	G/H
center, hypercenter	C₂×C₁₉	D₇₉⋊C₃
commutator, cosocle, hypocenter	C₇₉	C₂²×C₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₁₉×C₇₉	C₂×C₃
LCS	G ▷ C₇₉
UCS	C₁ ◁ C₂×C₁₉

40 conjugacy classes of subgroups.

μ_t(G) = 3002

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18012, 30);