C₁₉×C₃⋊(D₂₉⋊C₇) #37529018

order	23142
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₉×C₃⋊(D₂₉⋊C₇)
unambiguous semidirect product	C₃⋊(C₁₉×D₂₉⋊C₇)
unambiguous semidirect product	D₈₇⋊(C₇×C₁₉)
unambiguous semidirect product	(C₂₉⋊C₇)⋊(D₃×C₁₉)
unambiguous semidirect product	(C₁₉×D₈₇)⋊C₇

	subgroup	G/H
center, hypercenter	C₁₉	C₃⋊(D₂₉⋊C₇)
commutator, cosocle, hypocenter	C₃×C₂₉	C₂×C₇×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₁₉×C₂₉	C₂×C₇
LCS	G ▷ C₃×C₂₉
UCS	C₁ ◁ C₁₉

32 conjugacy classes of subgroups.

μ_t(G) = 1653

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23142, 27);