Finite Group Databasebeta

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C₂²×C₃×C₁₃×C₁₉⋊C₃ #22580389

order	8892
isoclinism	isoclinic class of C₁₉⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃²×C₁₃ · Schur multiplier (H₂) = C₂×C₃

Aliases

C₂²×C₃×C₁₃×C₁₉⋊C₃

Splittings

Fitting, socle	C₂²×C₃×C₁₃×C₁₉ ⋊ C₃
derived, Sylow	C₁₉ ⋊ C₂²×C₃²×C₁₃
Hall	C₂²×C₁₃×C₁₉ ⋊ C₃²
Hall	C₁₃×C₁₉ ⋊ C₂²×C₃²
Hall	C₂²×C₁₉ ⋊ C₃²×C₁₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂²×C₃×C₁₃	C₁₉⋊C₃
commutator, hypocenter	C₁₉	C₂²×C₃²×C₁₃
Frattini	C₁	G
Fitting, socle	C₂²×C₃×C₁₃×C₁₉	C₃
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂²×C₃×C₁₃

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1404 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8892, 292);