C₁₉×ΓL(1,𝔽₈)×C₅⋊D₅ #34093047

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

Aliases

direct product	C₁₉×ΓL(1,𝔽₈)×C₅⋊D₅
unambiguous semidirect product	C₅⋊(D₅×C₁₉×ΓL(1,𝔽₈))

	subgroup	G/H
center, hypercenter	C₁₉	ΓL(1,𝔽₈)×C₅⋊D₅
commutator, cosocle, hypocenter	C₅²×C₇	C₂×C₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₅²×C₇×C₁₉	C₂×C₃
LCS	G ▷ C₅²×C₇
UCS	C₁ ◁ C₁₉

128 conjugacy classes of subgroups.

μ_t(G) = 3325

1330 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19950, 86);