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C₅×D₃×D₇×C₁₉ #22547710

order	7980
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₅×D₃×D₇×C₁₉
unambiguous semidirect product	(D₃×C₇)⋊(C₂×C₅×C₁₉)
unambiguous semidirect product	(C₃×D₇)⋊(C₂×C₅×C₁₉)
unambiguous semidirect product	D₂₁⋊(C₂×C₅×C₁₉)

Splittings

Subgroups

	subgroup	G/H
center, hypercenter	C₅×C₁₉	D₃×D₇
commutator, hypocenter	C₃×C₇	C₂²×C₅×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₁₉	C₂²
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₅×C₁₉

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1425 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅×D₇×D₉×C₁₉, C₅×D₃×C₁₉×AGL(1,𝔽₇), C₅×D₃×#11716325, …
maximal normal subgroup of	C₅×D₃×C₁₉×AGL(1,𝔽₇), C₅×D₃×#11716325, C₅×D₃×#11716326, …
maximal quotient of	C₅×D₇×D₉×C₁₉, C₃×C₅×D₃×D₇×C₁₉, C₅×D₃×C₁₉×D₂₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7980, 135);