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C₉×C₅₉⋊C₂₉ #29507034

order	15399
automorphism	?
homology	Abelianization (H₁) = C₉×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×C₅₉⋊C₂₉
unambiguous semidirect product	C₅₉⋊(C₉×C₂₉)
unambiguous semidirect product	(C₉×C₅₉)⋊C₂₉

Splittings

Fitting, Hall	C₉×C₅₉ ⋊ C₂₉
derived, Sylow	C₅₉ ⋊ C₉×C₂₉

Subgroups

	subgroup	G/H
center, hypercenter	C₉	C₅₉⋊C₂₉
commutator, hypocenter	C₅₉	C₉×C₂₉
Frattini	C₃	C₃×C₅₉⋊C₂₉
Fitting	C₉×C₅₉	C₂₉
socle, cosocle	C₃×C₅₉	C₃×C₂₉
prime radical	C₃×C₅₉⋊C₂₉	C₃
LCS	G ▷ C₅₉
UCS	C₁ ◁ C₉

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 531

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₉×C₅₉⋊C₂₉, C₉×AGL(1,𝔽₅₉), D₉×C₅₉⋊C₂₉, …
maximal normal subgroup of	C₂×C₉×C₅₉⋊C₂₉, C₉×AGL(1,𝔽₅₉), D₉×C₅₉⋊C₂₉, …
maximal quotient of	C₂×C₉×C₅₉⋊C₂₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15399, 2);