Finite Group Databasebeta

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C₁₃×D₉×C₄₉ #26039378

order	11466
isoclinism	isoclinic class of D₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₃×C₄₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₃×D₉×C₄₉
unambiguous semidirect product	C₉⋊(C₂×C₁₃×C₄₉)

Splittings

Fitting, Hall	C₉×C₁₃×C₄₉ ⋊ C₂
derived, Sylow	C₉ ⋊ C₂×C₁₃×C₄₉
Hall	C₉×C₄₉ ⋊ C₂×C₁₃
Hall	C₉×C₁₃ ⋊ C₂×C₄₉

Subgroups

	subgroup	G/H
center, hypercenter	C₁₃×C₄₉	D₉
commutator, hypocenter	C₉	C₂×C₁₃×C₄₉
Frattini	C₃×C₇	D₃×C₇×C₁₃
Fitting	C₉×C₁₃×C₄₉	C₂
socle	C₃×C₇×C₁₃	D₃×C₇
prime radical	C₇×C₁₃×D₉	C₇
cosocle	C₇×C₉	C₂×C₇×C₁₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₁₃×C₄₉

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3822 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₉×D₁₃×C₄₉, C₁₃×D₉×D₄₉, D₉×D₆₃₇, …
maximal normal subgroup of	D₉×D₁₃×C₄₉, C₁₃×D₉×D₄₉, D₉×D₆₃₇, …
maximal quotient of	C₁₃×Dic₉×C₄₉, C₂×C₁₃×D₉×C₄₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11466, 21);