C₅×C₁₉×C₂₉⋊C₇ #34064329

order	19285
automorphism	?
homology	Abelianization (H₁) = C₅×C₇×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×C₁₉×C₂₉⋊C₇
unambiguous semidirect product	C₂₉⋊(C₅×C₇×C₁₉)
unambiguous semidirect product	(C₅×C₂₉)⋊(C₇×C₁₉)
unambiguous semidirect product	(C₁₉×C₂₉)⋊(C₅×C₇)
unambiguous semidirect product	(C₅×C₁₉×C₂₉)⋊C₇

	subgroup	G/H
center, hypercenter	C₅×C₁₉	C₂₉⋊C₇
commutator, cosocle, hypocenter	C₂₉	C₅×C₇×C₁₉
Frattini	C₁	G
Fitting, socle	C₅×C₁₉×C₂₉	C₇
LCS	G ▷ C₂₉
UCS	C₁ ◁ C₅×C₁₉

16 conjugacy classes of subgroups.

μ_t(G) = 2755

1045 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19285, 2);