Finite Group Databasebeta

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C₁₉×C₃⋊Dic₃₉ #22580232

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

Aliases

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

Splittings

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

Subgroups

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

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2280 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8892, 135);