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D₃₉×C₈₉ #20294248

order	6942
isoclinism	isoclinic class of D₃₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₈₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₃₉×C₈₉
unambiguous semidirect product	C₃⋊(D₁₃×C₈₉)
unambiguous semidirect product	C₁₃⋊(D₃×C₈₉)

Splittings

Fitting, socle, Hall	C₃×C₁₃×C₈₉ ⋊ C₂
derived, Hall	C₃×C₁₃ ⋊ C₂×C₈₉
Hall	C₁₃×C₈₉ ⋊ D₃
Hall	C₃×C₈₉ ⋊ D₁₃
Sylow	C₁₃ ⋊ D₃×C₈₉
Sylow	C₃ ⋊ D₁₃×C₈₉

Subgroups

	subgroup	G/H
center, hypercenter	C₈₉	D₃₉
commutator, hypocenter	C₃×C₁₃	C₂×C₈₉
Frattini	C₁	G
Fitting, socle	C₃×C₁₃×C₈₉	C₂
LCS	G ▷ C₃×C₁₃
UCS	C₁ ◁ C₈₉

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1869 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₃₉×D₈₉, D₃×D₁₃×C₈₉, D₃₉⋊D₈₉, …
maximal normal subgroup of	D₃₉×D₈₉, D₃×D₁₃×C₈₉, D₃₉⋊D₈₉, …
maximal quotient of	C₈₉×Dic₃₉, C₂×D₃₉×C₈₉, C₈₉×D₁₁₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6942, 8);