Finite Group Databasebeta

← Prev (#19152801) Next (#19152803) →

C₃×C₅×C₁₉×Dic₅ #19152802

order	5700
isoclinism	isoclinic class of D₅
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₅×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

C₃×C₅×C₁₉×Dic₅

Splittings

derived	C₅ ⋊ C₃×C₄×C₅×C₁₉
Hall	C₃×C₅²×C₁₉ ⋊ C₄
Hall	C₅²×C₁₉ ⋊ C₃×C₄
Hall	C₃×C₅² ⋊ C₄×C₁₉
Sylow	C₅² ⋊ C₃×C₄×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅×C₁₉	D₅
commutator, hypocenter	C₅	C₃×C₄×C₅×C₁₉
Frattini	C₂	C₃×C₅×D₅×C₁₉
Fitting, socle	C₂×C₃×C₅²×C₁₉	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₅×C₁₉

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2280 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅×Dic₅×#4294, C₅×C₉×C₁₉×Dic₅, C₃×C₅×Dic₅×C₁₉⋊C₃, …
maximal normal subgroup of	C₅×Dic₅×#4294, C₅×C₉×C₁₉×Dic₅, C₃×C₅×Dic₅×C₁₉⋊C₃, …
maximal quotient of	C₅×C₉×C₁₉×Dic₅, C₃²×C₅×C₁₉×Dic₅, C₃×C₅×C₁₉×Dic₁₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5700, 59);