C₅×D₁₃×D₁₉⋊C₃ #28414775

order	14820
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₅ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₅×D₁₃×D₁₉⋊C₃
unambiguous semidirect product	D₁₉⋊(C₃×C₅×D₁₃)
unambiguous semidirect product	(C₁₃×D₁₉⋊C₃)⋊(C₂×C₅)
unambiguous semidirect product	(D₁₃×C₁₉⋊C₃)⋊(C₂×C₅)
unambiguous semidirect product	((C₁₉⋊C₃)⋊D₁₃)⋊(C₂×C₅)

	subgroup	G/H
center, hypercenter	C₅	D₁₃×D₁₉⋊C₃
commutator, cosocle, hypocenter	C₁₃×C₁₉	C₂²×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₁₃×C₁₉	C₂²×C₃
LCS	G ▷ C₁₃×C₁₉
UCS	C₁ ◁ C₅

80 conjugacy classes of subgroups.

μ_t(G) = 1235

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14820, 61);