Finite Group Databasebeta

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C₃×Dic₁₃×C₁₉⋊C₃ #22580202

order	8892
automorphism	?
homology	Abelianization (H₁) = C₃²×C₄ · Schur multiplier (H₂) = C₃

Aliases

C₃×Dic₁₃×C₁₉⋊C₃

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃	D₁₃×C₁₉⋊C₃
commutator, hypocenter	C₁₃×C₁₉	C₃²×C₄
Frattini	C₂	C₃×D₁₃×C₁₉⋊C₃
Fitting, socle	C₂×C₃×C₁₃×C₁₉	C₂×C₃
LCS	G ▷ C₁₃×C₁₉
UCS	C₁ ◁ C₂×C₃

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

432 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8892, 105);