Finite Group Databasebeta

← Prev (#23758448) Next (#23758450) →

C₁₃×D₄₃⋊C₉ #23758449

order	10062
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₃×D₄₃⋊C₉
unambiguous semidirect product	D₄₃⋊(C₉×C₁₃)
unambiguous semidirect product	(C₄₃⋊C₉)⋊(C₂×C₁₃)

Splittings

derived, Sylow	C₄₃ ⋊ C₂×C₉×C₁₃
Hall	C₁₃×C₄₃⋊C₉ ⋊ C₂
Hall	C₁₃×D₄₃ ⋊ C₉
Hall	C₁₃×C₄₃ ⋊ C₂×C₉
Hall	C₄₃⋊C₉ ⋊ C₂×C₁₃
Hall	D₄₃ ⋊ C₉×C₁₃

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₃	D₄₃⋊C₃
commutator, hypocenter	C₄₃	C₂×C₉×C₁₃
Frattini	C₃	C₁₃×D₄₃⋊C₃
Fitting, socle	C₃×C₁₃×C₄₃	C₂×C₃
prime radical	C₃×C₁₃×D₄₃	C₃
cosocle	C₃×C₄₃	C₂×C₃×C₁₃
LCS	G ▷ C₄₃
UCS	C₁ ◁ C₃×C₁₃

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

507 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₁₃×D₄₃⋊C₉, C₂×C₁₃×D₄₃⋊C₉
maximal normal subgroup of	D₁₃×D₄₃⋊C₉, C₂×C₁₃×D₄₃⋊C₉
maximal quotient of	C₁₃×Dic₄₃⋊C₉, C₂×C₁₃×D₄₃⋊C₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10062, 13);