Finite Group Databasebeta

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C₂×C₁₉×#11758281 #49152149

order	37278
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

C₂×C₁₉×#11758281

Splittings

Fitting, socle, Hall	C₂×C₁₉×C₁₀₉ ⋊ C₉
derived, Sylow	C₁₀₉ ⋊ C₂×C₉×C₁₉
Hall	C₁₉×C₁₀₉ ⋊ C₂×C₉
Hall	C₂×C₁₀₉ ⋊ C₉×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₉	#11758281
commutator, hypocenter	C₁₀₉	C₂×C₉×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₁₉×C₁₀₉	C₉
prime radical	C₂×C₁₉×C₁₀₉⋊C₃	C₃
cosocle	C₁₀₉⋊C₃	C₂×C₃×C₁₉
LCS	G ▷ C₁₀₉
UCS	C₁ ◁ C₂×C₁₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 4142

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37278, 65);