C₁₃×C₁₉×D₄₉ #37564138

order	24206
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₃×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₃×C₁₉×D₄₉
unambiguous semidirect product	C₄₉⋊(C₂×C₁₃×C₁₉)

	subgroup	G/H
center, hypercenter	C₁₃×C₁₉	D₄₉
commutator, cosocle, hypocenter	C₄₉	C₂×C₁₃×C₁₉
Frattini	C₇	C₁₃×D₇×C₁₉
Fitting	C₁₃×C₁₉×C₄₉	C₂
socle	C₇×C₁₃×C₁₉	D₇
LCS	G ▷ C₄₉
UCS	C₁ ◁ C₁₃×C₁₉

24 conjugacy classes of subgroups.

μ_t(G) = 12103

6422 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24206, 5);