C₃×C₅₉×C₄₉⋊C₃ #39907292

order	26019
automorphism	?
homology	Abelianization (H₁) = C₃²×C₅₉ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃×C₅₉×C₄₉⋊C₃
unambiguous semidirect product	C₄₉⋊(C₃²×C₅₉)
unambiguous semidirect product	(C₃×C₄₉)⋊(C₃×C₅₉)
unambiguous semidirect product	(C₄₉×C₅₉)⋊C₃²
unambiguous semidirect product	(C₃×C₄₉×C₅₉)⋊C₃

	subgroup	G/H
center, hypercenter	C₃×C₅₉	C₄₉⋊C₃
commutator, cosocle, hypocenter	C₄₉	C₃²×C₅₉
Frattini	C₇	C₃×ΓL(1,𝔽₈)×C₅₉
Fitting	C₃×C₄₉×C₅₉	C₃
socle	C₃×C₇×C₅₉	ΓL(1,𝔽₈)
LCS	G ▷ C₄₉
UCS	C₁ ◁ C₃×C₅₉

36 conjugacy classes of subgroups.

μ_t(G) = 8673

3363 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26019, 4);