Finite Group Databasebeta

← Prev (#28413649) Next (#28413651) →

C₉×C₁₉×D₄₃ #28413650

order	14706
isoclinism	isoclinic class of D₄₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

C₉×C₁₉×D₄₃

Splittings

Fitting, Hall	C₉×C₁₉×C₄₃ ⋊ C₂
derived, Sylow	C₄₃ ⋊ C₂×C₉×C₁₉
Hall	C₁₉×C₄₃ ⋊ C₂×C₉
Hall	C₉×C₄₃ ⋊ C₂×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₁₉	D₄₃
commutator, hypocenter	C₄₃	C₂×C₉×C₁₉
Frattini	C₃	C₃×C₁₉×D₄₃
Fitting	C₉×C₁₉×C₄₃	C₂
socle	C₃×C₁₉×C₄₃	C₂×C₃
prime radical	C₃×C₁₉×D₄₃	C₃
cosocle	C₃×C₄₃	C₂×C₃×C₁₉
LCS	G ▷ C₄₃
UCS	C₁ ◁ C₉×C₁₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 7353

Conjugacy classes & character table

3933 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₁₉×D₄₃, D₉×C₁₉×D₄₃, D₄₃×D₁₇₁, …
maximal normal subgroup of	C₉×D₁₉×D₄₃, D₉×C₁₉×D₄₃, D₄₃×D₁₇₁, …
maximal quotient of	C₉×C₁₉×Dic₄₃, C₂×C₉×C₁₉×D₄₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14706, 6);