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C₃×D₁₉×C₅⋊D₅ #19152860

order	5700
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂×C₅

Aliases

C₃×D₁₉×C₅⋊D₅

Splittings

Fitting, socle, Hall	C₃×C₅²×C₁₉ ⋊ C₂²
derived, Hall	C₅²×C₁₉ ⋊ C₂²×C₃
Hall	C₃×C₅² ⋊ C₂×D₁₉
Hall	C₃×C₁₉ ⋊ C₂×C₅⋊D₅
Sylow	C₅² ⋊ C₂×C₃×D₁₉
Sylow	C₁₉ ⋊ C₂×C₃×C₅⋊D₅

Subgroups

	subgroup	G/H
center, hypercenter	C₃	D₁₉×C₅⋊D₅
commutator, hypocenter	C₅²×C₁₉	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₉	C₂²
LCS	G ▷ C₅²×C₁₉
UCS	C₁ ◁ C₃

160 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

462 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₅⋊D₅×#4294⋊C₂, #22555508⋊C₂, D₁₉×(C₅⋊D₅)⋊C₉, …
maximal normal subgroup of	C₅⋊D₅×#4294⋊C₂, #22555508⋊C₂, D₁₉×(C₅⋊D₅)⋊C₉, …
maximal quotient of	C₉×D₁₉×C₅⋊D₅, C₃²×D₁₉×C₅⋊D₅, C₃×D₁₉×C₃⋊(C₅⋊D₅), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5700, 117);