C₃×C₅×C₁₃×C₄₉⋊C₃ #43270909

order	28665
automorphism	?
homology	Abelianization (H₁) = C₃²×C₅×C₁₃ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃×C₅×C₁₃×C₄₉⋊C₃
unambiguous semidirect product	C₄₉⋊(C₃²×C₅×C₁₃)
unambiguous semidirect product	(C₃×C₄₉)⋊(C₃×C₅×C₁₃)
unambiguous semidirect product	(C₅×C₄₉)⋊(C₃²×C₁₃)
unambiguous semidirect product	(C₃×C₅×C₄₉)⋊(C₃×C₁₃)

	subgroup	G/H
center, hypercenter	C₃×C₅×C₁₃	C₄₉⋊C₃
commutator, cosocle, hypocenter	C₄₉	C₃²×C₅×C₁₃
Frattini	C₇	C₃×C₅×C₁₃×ΓL(1,𝔽₈)
Fitting	C₃×C₅×C₁₃×C₄₉	C₃
socle	C₃×C₅×C₇×C₁₃	ΓL(1,𝔽₈)
LCS	G ▷ C₄₉
UCS	C₁ ◁ C₃×C₅×C₁₃

72 conjugacy classes of subgroups.

μ_t(G) = 9555

3705 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28665, 10);