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C₅×C₁₉×C₃₁⋊C₃ #22579546

order	8835
isoclinism	isoclinic class of C₃₁⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₃×C₅×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×C₁₉×C₃₁⋊C₃
unambiguous semidirect product	(C₅×C₃₁)⋊(C₃×C₁₉)

Splittings

Fitting, socle, Hall	C₅×C₁₉×C₃₁ ⋊ C₃
derived, Sylow	C₃₁ ⋊ C₃×C₅×C₁₉
Hall	C₁₉×C₃₁ ⋊ C₃×C₅
Hall	C₅×C₃₁ ⋊ C₃×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₅×C₁₉	C₃₁⋊C₃
commutator, hypocenter	C₃₁	C₃×C₅×C₁₉
Frattini	C₁	G
Fitting, socle	C₅×C₁₉×C₃₁	C₃
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₅×C₁₉

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1235 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₅×C₁₉×C₃₁⋊C₃, C₅×C₁₉×D₃₁⋊C₃, C₅×D₁₉×C₃₁⋊C₃, …
maximal normal subgroup of	C₂×C₅×C₁₉×C₃₁⋊C₃, C₅×C₁₉×D₃₁⋊C₃, C₅×D₁₉×C₃₁⋊C₃, …
maximal quotient of	C₂×C₅×C₁₉×C₃₁⋊C₃, C₅×C₁₉×C₃₁⋊C₉, C₃×C₅×C₁₉×C₃₁⋊C₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8835, 3);