Finite Group Databasebeta

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C₅×Dic₃×C₁₉ #11765880

order	1140
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₄×C₅×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×Dic₃×C₁₉
unambiguous semidirect product	C₃⋊(C₄×C₅×C₁₉)

Splittings

derived, Sylow	C₃ ⋊ C₄×C₅×C₁₉
Hall	C₃×C₅×C₁₉ ⋊ C₄
Hall	C₃×C₁₉ ⋊ C₄×C₅
Hall	C₃×C₅ ⋊ C₄×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₅×C₁₉	D₃
commutator, hypocenter	C₃	C₄×C₅×C₁₉
Frattini	C₂	C₅×D₃×C₁₉
Fitting, socle, prime radical	C₂×C₃×C₅×C₁₉	C₂
cosocle	C₂×C₃	C₂×C₅×C₁₉
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₅×C₁₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 1140

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₅×C₁₉×Dic₉, C₅×Dic₃×C₁₉⋊C₃, C₃×C₅×Dic₃×C₁₉, …
maximal normal subgroup of	C₅×Dic₃×C₁₉⋊C₃, C₃×C₅×Dic₃×C₁₉, C₅×C₁₁×Dic₃×C₁₉, …
maximal quotient of	C₅×C₁₉×Dic₉, C₃×C₅×Dic₃×C₁₉, C₅×C₁₉×C₃⋊Dic₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1140, 8);