Finite Group Databasebeta

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C₉×C₁₉×#5997 #45691666

order	33516
automorphism	?
homology	Abelianization (H₁) = C₄×C₉×C₁₉ · Schur multiplier (H₂) = C₇

Aliases

C₉×C₁₉×#5997

Splittings

Fitting, Hall	C₇²×C₉×C₁₉ ⋊ C₄
derived, Sylow	C₇² ⋊ C₄×C₉×C₁₉
Hall	C₇²×C₁₉ ⋊ C₄×C₉
Hall	C₇²×C₉ ⋊ C₄×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₁₉	#5997
commutator, hypocenter	C₇²	C₄×C₉×C₁₉
Frattini	C₃	C₃×C₁₉×#5997
Fitting	C₇²×C₉×C₁₉	C₄
socle	C₃×C₇²×C₁₉	C₃×C₄
prime radical	C₃×C₁₉×C₇⋊D₇	C₂×C₃
cosocle	C₃×C₇⋊D₇	C₂×C₃×C₁₉
LCS	G ▷ C₇²
UCS	C₁ ◁ C₉×C₁₉

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 2394

Conjugacy classes & character table

2736 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 464);