C₅×C₇×D₅×C₁₉⋊C₃ #34093024

order	19950
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₅×C₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×C₇×D₅×C₁₉⋊C₃
unambiguous semidirect product	C₅⋊(C₂×C₅×C₇×C₁₉⋊C₃)
unambiguous semidirect product	(D₅×C₁₉)⋊(C₃×C₅×C₇)
unambiguous semidirect product	(C₅×D₅×C₁₉)⋊(C₃×C₇)

	subgroup	G/H
center, hypercenter	C₅×C₇	D₅×C₁₉⋊C₃
commutator, cosocle, hypocenter	C₅×C₁₉	C₂×C₃×C₅×C₇
Frattini	C₁	G
Fitting, socle	C₅²×C₇×C₁₉	C₂×C₃
LCS	G ▷ C₅×C₁₉
UCS	C₁ ◁ C₅×C₇

80 conjugacy classes of subgroups.

μ_t(G) = 1330

1260 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19950, 63);