D₁₃×D₇₉⋊C₉ #49149404

order	36972
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₁₃×D₇₉⋊C₉
unambiguous semidirect product	D₇₉⋊(C₉×D₁₃)
unambiguous semidirect product	(C₁₃×D₇₉⋊C₉)⋊C₂
unambiguous semidirect product	(D₁₃×C₇₉⋊C₉)⋊C₂
unambiguous semidirect product	((C₇₉⋊C₉)⋊D₁₃)⋊C₂

	subgroup	G/H
center, Frattini, hypercenter	C₃	D₁₃×D₇₉⋊C₃
commutator, hypocenter	C₁₃×C₇₉	C₂²×C₉
Fitting, socle, cosocle	C₃×C₁₃×C₇₉	C₂²×C₃
prime radical	C₃×D₁₃×D₇₉	C₃
LCS	G ▷ C₁₃×C₇₉
UCS	C₁ ◁ C₃

60 conjugacy classes of subgroups.

μ_t(G) = 9243

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36972, 52);