Finite Group Databasebeta

← Prev (#19152855) Next (#19152857) →

C₃×C₁₉×#1044 #19152856

order	5700
isoclinism	isoclinic class of #1044
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₁₉ · Schur multiplier (H₂) = C₅

Aliases

C₃×C₁₉×#1044

Splittings

Fitting, socle, Hall	C₃×C₅²×C₁₉ ⋊ C₄
derived, Sylow	C₅² ⋊ C₃×C₄×C₁₉
Hall	C₅²×C₁₉ ⋊ C₃×C₄
Hall	C₃×C₅² ⋊ C₄×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₉	#1044
commutator, hypocenter	C₅²	C₃×C₄×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₉	C₄
LCS	G ▷ C₅²
UCS	C₁ ◁ C₃×C₁₉

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

570 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#1044×#4294, C₉×C₁₉×#1044, C₃×C₁₉⋊C₃×#1044, …
maximal normal subgroup of	#1044×#4294, C₉×C₁₉×#1044, C₃×C₁₉⋊C₃×#1044, …
maximal quotient of	C₉×C₁₉×#1044, C₃²×C₁₉×#1044, C₃×C₁₉×C₃⋊#1044

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5700, 113);