Finite Group Databasebeta

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C₉×C₁₃×D₄₉ #26039376

order	11466
isoclinism	isoclinic class of D₄₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

C₉×C₁₃×D₄₉

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₁₃	D₄₉
commutator, hypocenter	C₄₉	C₂×C₉×C₁₃
Frattini	C₃×C₇	C₃×C₁₃×D₇
Fitting	C₉×C₁₃×C₄₉	C₂
socle	C₃×C₇×C₁₃	C₃×D₇
prime radical	C₃×C₁₃×D₄₉	C₃
cosocle	C₃×C₄₉	C₂×C₃×C₁₃
LCS	G ▷ C₄₉
UCS	C₁ ◁ C₉×C₁₃

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3042 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₁₃×D₄₉, C₁₃×D₉×D₄₉, D₄₉×D₁₁₇, …
maximal normal subgroup of	C₉×D₁₃×D₄₉, C₁₃×D₉×D₄₉, D₄₉×D₁₁₇, …
maximal quotient of	C₉×C₁₃×Dic₄₉, C₂×C₉×C₁₃×D₄₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11466, 19);