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D₃×C₁₉×C₇₃ #22552237

order	8322
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₉×C₇₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₃×C₁₉×C₇₃
unambiguous semidirect product	C₃⋊(C₂×C₁₉×C₇₃)

Splittings

Fitting, socle, Hall	C₃×C₁₉×C₇₃ ⋊ C₂
derived, Sylow	C₃ ⋊ C₂×C₁₉×C₇₃
Hall	C₃×C₇₃ ⋊ C₂×C₁₉
Hall	C₃×C₁₉ ⋊ C₂×C₇₃

Subgroups

	subgroup	G/H
center, hypercenter	C₁₉×C₇₃	D₃
commutator, hypocenter	C₃	C₂×C₁₉×C₇₃
Frattini	C₁	G
Fitting, socle	C₃×C₁₉×C₇₃	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₁₉×C₇₃

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4161 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₃×C₁₉×D₇₃, D₃×D₁₉×C₇₃, D₃×D₁₃₈₇, …
maximal normal subgroup of	D₃×C₁₉×D₇₃, D₃×D₁₉×C₇₃, D₃×D₁₃₈₇, …
maximal quotient of	Dic₃×C₁₉×C₇₃, C₂×D₃×C₁₉×C₇₃, D₉×C₁₉×C₇₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8322, 9);