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C₁₃×Dic₁₃⋊C₉ #20258751

order	6084
isoclinism	isoclinic class of D₁₃⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₄×C₉×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₃×Dic₁₃⋊C₉
unambiguous semidirect product	Dic₁₃⋊(C₉×C₁₃)

Splittings

derived	C₁₃ ⋊ C₄×C₉×C₁₃
Hall	C₁₃×C₁₃⋊C₉ ⋊ C₄
Hall	C₁₃×Dic₁₃ ⋊ C₉
Sylow	C₁₃² ⋊ C₄×C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₃	D₁₃⋊C₃
commutator, hypocenter	C₁₃	C₄×C₉×C₁₃
Frattini	C₂×C₃	C₁₃×D₁₃⋊C₃
Fitting, socle	C₂×C₃×C₁₃²	C₂×C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₃×C₁₃

44 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

624 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₅×C₁₃×Dic₁₃⋊C₉, C₁₃×Dic₆₅⋊C₉, C₁₃×#63120⋊C₉
maximal normal subgroup of	C₅×C₁₃×Dic₁₃⋊C₉
maximal quotient of	C₅×C₁₃×Dic₁₃⋊C₉, C₁₃×Dic₆₅⋊C₉, C₁₃×#63120⋊C₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6084, 58);