Finite Group Databasebeta

← Prev (#34037339) Next (#34037341) →

C₁₃×C₁₉×Dic₁₉ #34037340

order	18772
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₃×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₃×C₁₉×Dic₁₉
unambiguous semidirect product	C₁₉⋊(C₄×C₁₃×C₁₉)

Splittings

derived	C₁₉ ⋊ C₄×C₁₃×C₁₉
Hall	C₁₃×C₁₉² ⋊ C₄
Sylow	C₁₉² ⋊ C₄×C₁₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₃×C₁₉	D₁₉
commutator, hypocenter	C₁₉	C₄×C₁₃×C₁₉
Frattini	C₂	C₁₃×C₁₉×D₁₉
Fitting, socle, prime radical	C₂×C₁₃×C₁₉²	C₂
cosocle	C₂×C₁₉	C₂×C₁₃×C₁₉
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂×C₁₃×C₁₉

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 988

Conjugacy classes & character table

5434 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18772, 13);