C₅×C₁₉⋊C₃×D₃₅ #34093038

order	19950
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₅ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×C₁₉⋊C₃×D₃₅
unambiguous semidirect product	C₅⋊(C₅×D₇×C₁₉⋊C₃)

	subgroup	G/H
center, hypercenter	C₅	C₁₉⋊C₃×D₃₅
commutator, cosocle, hypocenter	C₅×C₇×C₁₉	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₅²×C₇×C₁₉	C₂×C₃
LCS	G ▷ C₅×C₇×C₁₉
UCS	C₁ ◁ C₅

80 conjugacy classes of subgroups.

μ_t(G) = 1330

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19950, 77);