Finite Group Databasebeta

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C₂×C₁₃×C₁₅₁⋊C₉ #47977451

order	35334
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂×C₁₃×C₁₅₁⋊C₉
unambiguous semidirect product	(C₂×C₁₅₁)⋊(C₉×C₁₃)

Splittings

derived, Sylow	C₁₅₁ ⋊ C₂×C₉×C₁₃
Hall	C₂×C₁₃×C₁₅₁ ⋊ C₉
Hall	C₁₃×C₁₅₁ ⋊ C₂×C₉
Hall	C₂×C₁₅₁ ⋊ C₉×C₁₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₃	C₁₅₁⋊C₃
commutator, hypocenter	C₁₅₁	C₂×C₉×C₁₃
Frattini	C₃	C₂×C₁₃×C₁₅₁⋊C₃
Fitting, socle, prime radical	C₂×C₃×C₁₃×C₁₅₁	C₃
cosocle	C₃×C₁₅₁	C₂×C₃×C₁₃
LCS	G ▷ C₁₅₁
UCS	C₁ ◁ C₂×C₃×C₁₃

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 35334

Conjugacy classes & character table

4134 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35334, 2);