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D₇×C₁₉×D₁₅ #22547720

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

Aliases

direct product	D₇×C₁₉×D₁₅
unambiguous semidirect product	(C₃×D₇)⋊(D₅×C₁₉)
unambiguous semidirect product	(C₅×D₇)⋊(D₃×C₁₉)

Splittings

Subgroups

	subgroup	G/H
center, hypercenter	C₁₉	D₇×D₁₅
commutator, hypocenter	C₃×C₅×C₇	C₂²×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₁₉	C₂²
LCS	G ▷ C₃×C₅×C₇
UCS	C₁ ◁ C₁₉

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

855 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₇×C₁₉×D₄₅, C₁₉×D₁₅×AGL(1,𝔽₇), D₁₅×#11716325, …
maximal normal subgroup of	C₁₉×D₁₅×AGL(1,𝔽₇), D₁₅×#11716325, D₁₅×#11716326, …
maximal quotient of	D₇×C₁₉×D₄₅, C₃×D₇×C₁₉×D₁₅, C₁₉×D₂₁⋊D₁₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7980, 145);