Finite Group Databasebeta

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C₂×C₉×#4296 #72210941

order	3078
isoclinism	isoclinic class of #4296
automorphism	?
homology	Abelianization (H₁) = C₂×C₉² · Schur multiplier (H₂) = C₉

Aliases

C₂×C₉×#4296

Splittings

Fitting	C₂×C₉×C₁₉ ⋊ C₉
derived, Sylow	C₁₉ ⋊ C₂×C₉²
Hall	C₂×C₁₉ ⋊ C₉²

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₉	#4296
commutator, hypocenter	C₁₉	C₂×C₉²
Frattini	C₃	C₂×C₃×#4296
Fitting	C₂×C₉×C₁₉	C₉
socle	C₂×C₃×C₁₉	C₃×C₉
prime radical	C₂×C₃×C₁₉⋊C₃	C₃²
cosocle	C₃×C₁₉⋊C₃	C₂×C₃²
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂×C₉

92 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

198 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₉×AGL(1,𝔽₁₉)
maximal normal subgroup of	C₂×C₉×AGL(1,𝔽₁₉)

GAP

Past the SmallGroups library coverage — no SmallGroups id.