C₂×C₂₉×C₁₆₉⋊C₃ #44440587

order	29406
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂×C₂₉×C₁₆₉⋊C₃
unambiguous semidirect product	(C₂×C₁₆₉)⋊(C₃×C₂₉)
unambiguous semidirect product	(C₂×C₂₉×C₁₆₉)⋊C₃

	subgroup	G/H
center, hypercenter	C₂×C₂₉	C₁₆₉⋊C₃
commutator, cosocle, hypocenter	C₁₆₉	C₂×C₃×C₂₉
Frattini	C₁₃	C₂×C₂₉×C₁₃⋊C₃
Fitting	C₂×C₂₉×C₁₆₉	C₃
socle	C₂×C₁₃×C₂₉	C₁₃⋊C₃
LCS	G ▷ C₁₆₉
UCS	C₁ ◁ C₂×C₂₉

24 conjugacy classes of subgroups.

μ_t(G) = 9802

3422 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29406, 2);