Finite Group Databasebeta

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C₂×C₁₉×C₇₉⋊C₃ #22583020

order	9006
isoclinism	isoclinic class of C₇₉⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂×C₁₉×C₇₉⋊C₃
unambiguous semidirect product	(C₂×C₇₉)⋊(C₃×C₁₉)

Splittings

Fitting, socle, Hall	C₂×C₁₉×C₇₉ ⋊ C₃
derived, Sylow	C₇₉ ⋊ C₂×C₃×C₁₉
Hall	C₁₉×C₇₉ ⋊ C₂×C₃
Hall	C₂×C₇₉ ⋊ C₃×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₉	C₇₉⋊C₃
commutator, hypocenter	C₇₉	C₂×C₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₁₉×C₇₉	C₃
LCS	G ▷ C₇₉
UCS	C₁ ◁ C₂×C₁₉

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1102 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄×C₁₉×C₇₉⋊C₃, C₁₉×(C₇₉⋊C₃)⋊C₄, Dic₁₉×C₇₉⋊C₃, …
maximal normal subgroup of	C₄×C₁₉×C₇₉⋊C₃, C₁₉×(C₇₉⋊C₃)⋊C₄, Dic₁₉×C₇₉⋊C₃, …
maximal quotient of	C₄×C₁₉×C₇₉⋊C₃, C₂²×C₁₉×C₇₉⋊C₃, C₂×C₁₉×C₇₉⋊C₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9006, 2);