C₃×C₁₉×(C₃₁⋊C₃)⋊C₅ #40997118

order	26505
automorphism	?
homology	Abelianization (H₁) = C₃²×C₅×C₁₉ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃×C₁₉×(C₃₁⋊C₃)⋊C₅
unambiguous semidirect product	(C₃₁⋊C₃)⋊(C₃×C₅×C₁₉)
unambiguous semidirect product	ΓL(1,𝔽₃₂)⋊(C₃²×C₁₉)
unambiguous semidirect product	(C₃×C₃₁⋊C₃)⋊(C₅×C₁₉)
unambiguous semidirect product	(C₃×ΓL(1,𝔽₃₂))⋊(C₃×C₁₉)
unambiguous semidirect product	(C₃×C₁₉×C₃₁⋊C₃)⋊C₅

	subgroup	G/H
center, hypercenter	C₃×C₁₉	(C₃₁⋊C₃)⋊C₅
commutator, cosocle, hypocenter	C₃₁	C₃²×C₅×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₁₉×C₃₁	C₃×C₅
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₃×C₁₉

48 conjugacy classes of subgroups.

μ_t(G) = 1767

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26505, 16);