Finite Group Databasebeta

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C₉×C₁₃×D₄₇ #24926945

order	10998
isoclinism	isoclinic class of D₄₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×C₁₃×D₄₇
unambiguous semidirect product	C₄₇⋊(C₂×C₉×C₁₃)

Splittings

Fitting, Hall	C₉×C₁₃×C₄₇ ⋊ C₂
derived, Sylow	C₄₇ ⋊ C₂×C₉×C₁₃
Hall	C₁₃×C₄₇ ⋊ C₂×C₉
Hall	C₉×C₄₇ ⋊ C₂×C₁₃

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₁₃	D₄₇
commutator, hypocenter	C₄₇	C₂×C₉×C₁₃
Frattini	C₃	C₃×C₁₃×D₄₇
Fitting	C₉×C₁₃×C₄₇	C₂
socle	C₃×C₁₃×C₄₇	C₂×C₃
prime radical	C₃×C₁₃×D₄₇	C₃
cosocle	C₃×C₄₇	C₂×C₃×C₁₃
LCS	G ▷ C₄₇
UCS	C₁ ◁ C₉×C₁₃

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2925 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₁₃×D₄₇, C₁₃×D₉×D₄₇, D₄₇×D₁₁₇, …
maximal normal subgroup of	C₉×D₁₃×D₄₇, C₁₃×D₉×D₄₇, D₄₇×D₁₁₇, …
maximal quotient of	C₉×C₁₃×Dic₄₇, C₂×C₉×C₁₃×D₄₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10998, 3);