C₅×C₁₉×C₅⋊AGL(1,𝔽₇) #34093025

order	19950
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₅×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×C₁₉×C₅⋊AGL(1,𝔽₇)
unambiguous semidirect product	C₅⋊(C₅×C₁₉×AGL(1,𝔽₇))
unambiguous semidirect product	ΓL(1,𝔽₈)⋊(C₅×D₅×C₁₉)
unambiguous semidirect product	D₃₅⋊(C₃×C₅×C₁₉)
unambiguous semidirect product	(C₅×D₃₅)⋊(C₃×C₁₉)

	subgroup	G/H
center, hypercenter	C₅×C₁₉	C₅⋊AGL(1,𝔽₇)
commutator, cosocle, hypocenter	C₅×C₇	C₂×C₃×C₅×C₁₉
Frattini	C₁	G
Fitting, socle	C₅²×C₇×C₁₉	C₂×C₃
LCS	G ▷ C₅×C₇
UCS	C₁ ◁ C₅×C₁₉

80 conjugacy classes of subgroups.

μ_t(G) = 1330

1615 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19950, 64);