Finite Group Databasebeta

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C₂×C₄₁×C₁₃⋊C₉ #23751127

order	9594
isoclinism	isoclinic class of C₁₃⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₄₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂×C₄₁×C₁₃⋊C₉
unambiguous semidirect product	(C₂×C₁₃)⋊(C₉×C₄₁)
unambiguous semidirect product	(C₂×C₁₃×C₄₁)⋊C₉

Splittings

derived, Sylow	C₁₃ ⋊ C₂×C₉×C₄₁
Hall	C₂×C₁₃×C₄₁ ⋊ C₉
Hall	C₁₃×C₄₁ ⋊ C₂×C₉
Hall	C₂×C₁₃ ⋊ C₉×C₄₁

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₄₁	C₁₃⋊C₃
commutator, hypocenter	C₁₃	C₂×C₉×C₄₁
Frattini	C₃	C₂×C₁₃⋊C₃×C₄₁
Fitting, socle, prime radical	C₂×C₃×C₁₃×C₄₁	C₃
cosocle	C₃×C₁₃	C₂×C₃×C₄₁
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₃×C₄₁

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1722 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄×C₄₁×C₁₃⋊C₉, C₁₃⋊C₉×Dic₄₁, C₄₁×Dic₁₃⋊C₉, …
maximal normal subgroup of	C₄×C₄₁×C₁₃⋊C₉, C₁₃⋊C₉×Dic₄₁, C₄₁×Dic₁₃⋊C₉, …
maximal quotient of	C₄×C₄₁×C₁₃⋊C₉, C₂²×C₄₁×C₁₃⋊C₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9594, 2);