C₇×C₁₉×C₃⋊AGL(1,𝔽₇) #30660804

order	16758
isoclinism	isoclinic class of C₃⋊AGL(1,𝔽₇)
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₇×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×C₁₉×C₃⋊AGL(1,𝔽₇)
unambiguous semidirect product	C₃⋊(C₇×C₁₉×AGL(1,𝔽₇))
unambiguous semidirect product	ΓL(1,𝔽₈)⋊(D₃×C₇×C₁₉)
unambiguous semidirect product	D₂₁⋊(C₃×C₇×C₁₉)

	subgroup	G/H
center, hypercenter	C₇×C₁₉	C₃⋊AGL(1,𝔽₇)
commutator, cosocle, hypocenter	C₃×C₇	C₂×C₃×C₇×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₁₉	C₂×C₃
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₇×C₁₉

76 conjugacy classes of subgroups.

μ_t(G) = 2394

1596 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16758, 331);