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D₅×C₁₉×C₁₉⋊C₃ #24925326

order	10830
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₅×C₁₉×C₁₉⋊C₃
unambiguous semidirect product	C₅⋊(C₂×C₁₉×C₁₉⋊C₃)
unambiguous semidirect product	(D₅×C₁₉)⋊(C₃×C₁₉)

Splittings

Fitting, socle, Hall	C₅×C₁₉² ⋊ C₂×C₃
derived	C₅×C₁₉ ⋊ C₂×C₃×C₁₉
Hall	C₅×C₁₉×C₁₉⋊C₃ ⋊ C₂
Hall	D₅×C₁₉² ⋊ C₃
Sylow	C₁₉² ⋊ C₃×D₅
Sylow	C₅ ⋊ C₂×C₁₉×C₁₉⋊C₃

Subgroups

	subgroup	G/H
center, hypercenter	C₁₉	D₅×C₁₉⋊C₃
commutator, cosocle, hypocenter	C₅×C₁₉	C₂×C₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₅×C₁₉²	C₂×C₃
LCS	G ▷ C₅×C₁₉
UCS	C₁ ◁ C₁₉

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

684 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×AGL(1,𝔽₅)×C₁₉⋊C₃, C₁₉×(C₁₉⋊C₃)⋊AGL(1,𝔽₅), (C₁₉⋊C₃)⋊(C₁₉⋊AGL(1,𝔽₅)), …
maximal normal subgroup of	C₁₉×AGL(1,𝔽₅)×C₁₉⋊C₃, C₁₉×(C₁₉⋊C₃)⋊AGL(1,𝔽₅), (C₁₉⋊C₃)⋊(C₁₉⋊AGL(1,𝔽₅)), …
maximal quotient of	C₁₉×Dic₅×C₁₉⋊C₃, C₂×D₅×C₁₉×C₁₉⋊C₃, D₅×C₁₉×#4294, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10830, 31);