Finite Group Databasebeta

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C₁₃×C₁₉⋊#157 #22580376

order	8892
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₃ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₁₃×C₁₉⋊#157
unambiguous semidirect product	C₁₉⋊(C₁₃×#157)

Splittings

Fitting, socle, Hall	C₃²×C₁₃×C₁₉ ⋊ C₄
derived, Hall	C₃²×C₁₉ ⋊ C₄×C₁₃
Hall	C₁₃×C₁₉ ⋊ #157
Hall	C₃²×C₁₃ ⋊ Dic₁₉
Sylow	C₁₉ ⋊ C₁₃×#157
Sylow	C₃² ⋊ C₁₃×Dic₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₁₃	C₁₉⋊#157
commutator, hypocenter	C₃²×C₁₉	C₄×C₁₃
Frattini	C₁	G
Fitting, socle	C₃²×C₁₃×C₁₉	C₄
LCS	G ▷ C₃²×C₁₉
UCS	C₁ ◁ C₁₃

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

780 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8892, 279);