Finite Group Databasebeta

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C₂²×C₃×C₁₉×C₁₃⋊C₃ #22580388

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

Aliases

C₂²×C₃×C₁₉×C₁₃⋊C₃

Splittings

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

Subgroups

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

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1596 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8892, 291);