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D₃×AGL(1,𝔽₁₉) #72214751

order	2052
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

D₃×AGL(1,𝔽₁₉)

Splittings

Fitting, socle, derived	C₃×C₁₉ ⋊ C₂²×C₉
Hall	C₃×#4296 ⋊ C₂²
Sylow	C₁₉ ⋊ C₂×D₃×C₉

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₁₉	C₂²×C₉
prime radical	D₃×D₁₉⋊C₃	C₃
cosocle	C₃×C₁₉⋊C₃	C₂²×C₃
LCS	G ▷ C₃×C₁₉
UCS	C₁

68 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

57 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	S₄×AGL(1,𝔽₁₉), C₃⋊D₃×AGL(1,𝔽₁₉), C₃×D₃×AGL(1,𝔽₁₉), …
maximal normal subgroup of	C₃×D₃×AGL(1,𝔽₁₉), C₂×D₃×AGL(1,𝔽₁₉)
maximal quotient of	S₄×AGL(1,𝔽₁₉), C₃⋊D₃×AGL(1,𝔽₁₉), C₃×D₃×AGL(1,𝔽₁₉), …
automorphism group of	D₅₇, C₃×C₁₉⋊C₃, D₃×D₁₉, …
holomorph of	C₃×C₁₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.