C₂×C₁₉×C₃⋊AGL(1,𝔽₇) #18012283

order	4788
isoclinism	isoclinic class of C₃⋊AGL(1,𝔽₇)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₁₉×C₃⋊AGL(1,𝔽₇)
unambiguous semidirect product	(C₂×C₃)⋊(C₁₉×AGL(1,𝔽₇))
unambiguous semidirect product	(C₂×ΓL(1,𝔽₈))⋊(D₃×C₁₉)
unambiguous semidirect product	(C₂×D₂₁)⋊(C₃×C₁₉)

	subgroup	G/H
center, hypercenter	C₂×C₁₉	C₃⋊AGL(1,𝔽₇)
commutator, cosocle, hypocenter	C₃×C₇	C₂²×C₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₇×C₁₉	C₂×C₃
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₂×C₁₉

88 conjugacy classes of subgroups.

μ_t(G) = 798

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4788, 199);