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C₉×D₁₀₄₃ #34037367

order	18774
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×D₁₀₄₃
unambiguous semidirect product	C₁₄₉⋊(C₉×D₇)

Splittings

Fitting, Hall	C₇×C₉×C₁₄₉ ⋊ C₂
derived, Hall	C₇×C₁₄₉ ⋊ C₂×C₉
Hall	C₉×C₁₄₉ ⋊ D₇
Sylow	C₁₄₉ ⋊ C₉×D₇
Hall	C₇×C₉ ⋊ D₁₄₉
Sylow	C₇ ⋊ C₉×D₁₄₉

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₁₀₄₃
commutator, hypocenter	C₇×C₁₄₉	C₂×C₉
Frattini	C₃	C₃×D₁₀₄₃
Fitting	C₇×C₉×C₁₄₉	C₂
socle, cosocle	C₃×C₇×C₁₄₉	C₂×C₃
prime radical	C₃×D₁₀₄₃	C₃
LCS	G ▷ C₇×C₁₄₉
UCS	C₁ ◁ C₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 9387

Conjugacy classes & character table

4707 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₇×D₁₄₉, D₉×D₁₀₄₃, D₆₃⋊D₁₄₉, …
maximal normal subgroup of	C₉×D₇×D₁₄₉, D₉×D₁₀₄₃, D₆₃⋊D₁₄₉, …
maximal quotient of	C₉×Dic₁₀₄₃, C₂×C₉×D₁₀₄₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18774, 5);