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C₂×C₁₃×D₁₃⋊C₉ #20258786

order	6084
isoclinism	isoclinic class of D₁₃⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₁₃×D₁₃⋊C₉
unambiguous semidirect product	D₁₃⋊(C₂×C₉×C₁₃)
unambiguous semidirect product	(C₂×D₁₃)⋊(C₉×C₁₃)
unambiguous semidirect product	(C₁₃⋊C₉)⋊(C₂²×C₁₃)
unambiguous semidirect product	(C₂×C₁₃⋊C₉)⋊(C₂×C₁₃)

Splittings

derived	C₁₃ ⋊ C₂²×C₉×C₁₃
Hall	C₁₃×C₁₃⋊C₉ ⋊ C₂²
Hall	C₂×C₁₃×D₁₃ ⋊ C₉
Sylow	C₁₃² ⋊ C₂²×C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₃	D₁₃⋊C₃
commutator, hypocenter	C₁₃	C₂²×C₉×C₁₃
Frattini	C₃	C₂×C₁₃×D₁₃⋊C₃
Fitting, socle	C₂×C₃×C₁₃²	C₂×C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₃×C₁₃

68 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

624 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₅×C₁₃×D₁₃⋊C₉, C₂×C₅×C₁₃×D₁₃⋊C₉, C₂×C₁₃×C₅⋊(D₁₃⋊C₉)
maximal normal subgroup of	C₂×C₅×C₁₃×D₁₃⋊C₉
maximal quotient of	D₅×C₁₃×D₁₃⋊C₉, C₂×C₅×C₁₃×D₁₃⋊C₉, C₂×C₁₃×C₅⋊(D₁₃⋊C₉)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6084, 93);