Finite Group Databasebeta

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C₃×C₁₉×Dic₃₉ #22580228

order	8892
isoclinism	isoclinic class of D₃₉
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×C₁₉×Dic₃₉
unambiguous semidirect product	C₃⋊(C₃×C₁₉×Dic₁₃)

Splittings

derived	C₃×C₁₃ ⋊ C₃×C₄×C₁₉
Hall	C₃²×C₁₃×C₁₉ ⋊ C₄
Hall	C₁₃×C₁₉ ⋊ C₃×Dic₃
Hall	C₃²×C₁₉ ⋊ Dic₁₃
Hall	C₃²×C₁₃ ⋊ C₄×C₁₉
Sylow	C₁₃ ⋊ C₃×Dic₃×C₁₉
Sylow	C₃² ⋊ C₁₉×Dic₁₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₉	D₃₉
commutator, hypocenter	C₃×C₁₃	C₃×C₄×C₁₉
Frattini	C₂	C₃×C₁₉×D₃₉
Fitting, socle	C₂×C₃²×C₁₃×C₁₉	C₂
LCS	G ▷ C₃×C₁₃
UCS	C₁ ◁ C₂×C₃×C₁₉

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2394 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8892, 131);