C₁₉×C₅⋊(D₂₉⋊C₇) #50310745

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

Aliases

direct product	C₁₉×C₅⋊(D₂₉⋊C₇)
unambiguous semidirect product	C₅⋊(C₁₉×D₂₉⋊C₇)
unambiguous semidirect product	(C₂₉⋊C₇)⋊(D₅×C₁₉)
unambiguous semidirect product	D₁₄₅⋊(C₇×C₁₉)
unambiguous semidirect product	(C₁₉×D₁₄₅)⋊C₇

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

32 conjugacy classes of subgroups.

μ_t(G) = 2755

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38570, 22);