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C₅×C₁₉×Dic₁₅ #19152808

order	5700
isoclinism	isoclinic class of D₁₅
automorphism	?
homology	Abelianization (H₁) = C₄×C₅×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×C₁₉×Dic₁₅
unambiguous semidirect product	C₃⋊(C₅×C₁₉×Dic₅)

Splittings

derived	C₃×C₅ ⋊ C₄×C₅×C₁₉
Hall	C₃×C₅²×C₁₉ ⋊ C₄
Hall	C₅²×C₁₉ ⋊ Dic₃
Hall	C₃×C₅² ⋊ C₄×C₁₉
Hall	C₃×C₁₉ ⋊ C₅×Dic₅
Sylow	C₅² ⋊ Dic₃×C₁₉
Sylow	C₃ ⋊ C₅×C₁₉×Dic₅

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₅×C₁₉	D₁₅
commutator, hypocenter	C₃×C₅	C₄×C₅×C₁₉
Frattini	C₂	C₅×C₁₉×D₁₅
Fitting, socle	C₂×C₃×C₅²×C₁₉	C₂
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₅×C₁₉

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1710 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₉×#11744607, C₅×C₁₉×Dic₄₅, C₅×C₁₉⋊C₃×Dic₁₅, …
maximal normal subgroup of	C₅×C₁₉⋊C₃×Dic₁₅, C₃×C₅×C₁₉×Dic₁₅
maximal quotient of	C₅×C₁₉×Dic₄₅, C₃×C₅×C₁₉×Dic₁₅, C₅×C₁₉×C₃⋊Dic₁₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5700, 65);