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C₄₁×Dic₁₃⋊C₃ #20264170

order	6396
isoclinism	isoclinic class of D₁₃⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₄₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₄₁×Dic₁₃⋊C₃
unambiguous semidirect product	Dic₁₃⋊(C₃×C₄₁)
unambiguous semidirect product	(C₄₁×Dic₁₃)⋊C₃

Splittings

derived, Sylow	C₁₃ ⋊ C₃×C₄×C₄₁
Hall	C₄₁×Dic₁₃ ⋊ C₃
Hall	C₁₃⋊C₃×C₄₁ ⋊ C₄
Hall	C₁₃×C₄₁ ⋊ C₃×C₄
Hall	Dic₁₃ ⋊ C₃×C₄₁
Hall	C₁₃⋊C₃ ⋊ C₄×C₄₁

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₄₁	D₁₃⋊C₃
commutator, hypocenter	C₁₃	C₃×C₄×C₄₁
Frattini	C₂	C₄₁×D₁₃⋊C₃
Fitting, socle	C₂×C₁₃×C₄₁	C₂×C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₄₁

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

656 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃×C₄₁×Dic₁₃⋊C₃, C₄₁×C₃⋊(Dic₁₃⋊C₃), C₅×C₄₁×Dic₁₃⋊C₃, …
maximal normal subgroup of	C₃×C₄₁×Dic₁₃⋊C₃, C₅×C₄₁×Dic₁₃⋊C₃, Dic₁₃⋊C₃×C₄₁⋊C₅
maximal quotient of	C₄₁×Dic₁₃⋊C₉, C₃×C₄₁×Dic₁₃⋊C₃, C₄₁×C₃⋊(Dic₁₃⋊C₃), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6396, 11);