C₁₃×C₁₉×C₂²⋊ΓL(1,𝔽₈) #35209176

order	20748
automorphism	?
homology	Abelianization (H₁) = C₃×C₁₃×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₁₃×C₁₉×C₂²⋊ΓL(1,𝔽₈)
unambiguous semidirect product	C₂²⋊(C₁₃×C₁₉×ΓL(1,𝔽₈))
unambiguous semidirect product	C₇⋊(A₄×C₁₃×C₁₉)

	subgroup	G/H
center, hypercenter	C₁₃×C₁₉	C₂²⋊ΓL(1,𝔽₈)
commutator, cosocle, hypocenter	C₂²×C₇	C₃×C₁₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₂²×C₇×C₁₃×C₁₉	C₃
LCS	G ▷ C₂²×C₇
UCS	C₁ ◁ C₁₃×C₁₉

40 conjugacy classes of subgroups.

μ_t(G) = 6916

2964 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20748, 404);