C₅×C₁₉×D₂₉⋊C₇ #50310741

order	38570
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₇×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×C₁₉×D₂₉⋊C₇
unambiguous semidirect product	D₂₉⋊(C₅×C₇×C₁₉)
unambiguous semidirect product	(C₂₉⋊C₇)⋊(C₂×C₅×C₁₉)
unambiguous semidirect product	(C₅×D₂₉)⋊(C₇×C₁₉)
unambiguous semidirect product	(C₁₉×D₂₉)⋊(C₅×C₇)
unambiguous semidirect product	(C₅×C₁₉×D₂₉)⋊C₇

	subgroup	G/H
center, hypercenter	C₅×C₁₉	D₂₉⋊C₇
commutator, cosocle, hypocenter	C₂₉	C₂×C₅×C₇×C₁₉
Frattini	C₁	G
Fitting, socle	C₅×C₁₉×C₂₉	C₂×C₇
LCS	G ▷ C₂₉
UCS	C₁ ◁ C₅×C₁₉

32 conjugacy classes of subgroups.

μ_t(G) = 2755

1520 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38570, 18);