Finite Group Databasebeta

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Dic₃×C₁₉×#3862 #45691936

order	33516
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₁₉ · Schur multiplier (H₂) = C₇

Aliases

direct product	Dic₃×C₁₉×#3862
unambiguous semidirect product	C₃⋊(C₄×C₁₉×#3862)

Splittings

derived	C₃×C₇² ⋊ C₃×C₄×C₁₉
Hall	C₃×C₁₉×#3862 ⋊ C₄
Hall	C₇²×C₁₉ ⋊ C₃×Dic₃
Hall	C₃×#3862 ⋊ C₄×C₁₉
Sylow	C₇² ⋊ C₃×Dic₃×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₉	D₃×#3862
commutator, hypocenter	C₃×C₇²	C₃×C₄×C₁₉
Frattini	C₂	D₃×C₁₉×#3862
Fitting, socle	C₂×C₃×C₇²×C₁₉	C₂×C₃
prime radical	C₂×C₃×C₁₉×#3862	C₂
cosocle	C₂×C₃×C₇²	C₂×C₃×C₁₉
LCS	G ▷ C₃×C₇²
UCS	C₁ ◁ C₂×C₁₉

136 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 4788

Conjugacy classes & character table

2166 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 734);