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C₉×D₁₃₃₉ #37562922

order	24102
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

C₉×D₁₃₃₉

Splittings

Fitting, Hall	C₉×C₁₃×C₁₀₃ ⋊ C₂
derived, Hall	C₁₃×C₁₀₃ ⋊ C₂×C₉
Hall	C₉×C₁₀₃ ⋊ D₁₃
Hall	C₉×C₁₃ ⋊ D₁₀₃
Sylow	C₁₀₃ ⋊ C₉×D₁₃
Sylow	C₁₃ ⋊ C₉×D₁₀₃

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₁₃₃₉
commutator, hypocenter	C₁₃×C₁₀₃	C₂×C₉
Frattini	C₃	C₃×D₁₃₃₉
Fitting	C₉×C₁₃×C₁₀₃	C₂
socle, cosocle	C₃×C₁₃×C₁₀₃	C₂×C₃
prime radical	C₃×D₁₃₃₉	C₃
LCS	G ▷ C₁₃×C₁₀₃
UCS	C₁ ◁ C₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 12051

Conjugacy classes & character table

6039 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24102, 8);