Finite Group Databasebeta

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C₂×C₉×D₁₉×C₄₉ #45691260

order	33516
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉×C₄₉ · Schur multiplier (H₂) = C₂

Aliases

C₂×C₉×D₁₉×C₄₉

Splittings

Fitting	C₂×C₉×C₁₉×C₄₉ ⋊ C₂
derived, Sylow	C₁₉ ⋊ C₂²×C₉×C₄₉
Hall	C₉×C₁₉×C₄₉ ⋊ C₂²
Hall	C₁₉×C₄₉ ⋊ C₂²×C₉
Hall	C₉×C₁₉ ⋊ C₂²×C₄₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₉×C₄₉	D₁₉
commutator, hypocenter	C₁₉	C₂²×C₉×C₄₉
Frattini	C₃×C₇	C₂×C₃×C₇×D₁₉
Fitting	C₂×C₉×C₁₉×C₄₉	C₂
socle	C₂×C₃×C₇×C₁₉	C₂×C₃×C₇
prime radical	C₂×C₃×C₇×D₁₉	C₃×C₇
cosocle	C₃×C₇×C₁₉	C₂²×C₃×C₇
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂×C₉×C₄₉

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 16758

Conjugacy classes & character table

9702 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 58);