C₂×C₂₉×C₁₂₁⋊C₅ #47975249

order	35090
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂×C₂₉×C₁₂₁⋊C₅
unambiguous semidirect product	(C₂×C₁₂₁)⋊(C₅×C₂₉)
unambiguous semidirect product	(C₂×C₂₉×C₁₂₁)⋊C₅

	subgroup	G/H
center, hypercenter	C₂×C₂₉	C₁₂₁⋊C₅
commutator, cosocle, hypocenter	C₁₂₁	C₂×C₅×C₂₉
Frattini	C₁₁	C₂×C₂₉×C₁₁⋊C₅
Fitting	C₂×C₂₉×C₁₂₁	C₅
socle	C₂×C₁₁×C₂₉	C₁₁⋊C₅
LCS	G ▷ C₁₂₁
UCS	C₁ ◁ C₂×C₂₉

24 conjugacy classes of subgroups.

μ_t(G) = 7018

1682 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35090, 2);