Finite Group Databasebeta

← Prev (#22583407) Next (#22583409) →

D₇×C₁₉×D₁₇ #22583408

order	9044
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₇×C₁₉×D₁₇
unambiguous semidirect product	(D₇×C₁₇)⋊(C₂×C₁₉)
unambiguous semidirect product	(C₇×D₁₇)⋊(C₂×C₁₉)
unambiguous semidirect product	D₁₁₉⋊(C₂×C₁₉)

Splittings

Fitting, socle, Hall	C₇×C₁₇×C₁₉ ⋊ C₂²
derived, Hall	C₇×C₁₇ ⋊ C₂²×C₁₉
Hall	C₁₇×C₁₉ ⋊ C₂×D₇
Hall	C₇×C₁₉ ⋊ C₂×D₁₇
Sylow	C₁₇ ⋊ C₂×D₇×C₁₉
Sylow	C₇ ⋊ C₂×C₁₉×D₁₇

Subgroups

	subgroup	G/H
center, hypercenter	C₁₉	D₇×D₁₇
commutator, hypocenter	C₇×C₁₇	C₂²×C₁₉
Frattini	C₁	G
Fitting, socle	C₇×C₁₇×C₁₉	C₂²
LCS	G ▷ C₇×C₁₇
UCS	C₁ ◁ C₁₉

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

950 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×D₁₇×AGL(1,𝔽₇), D₁₇×#11716325, D₁₇×#11716326, …
maximal normal subgroup of	C₁₉×D₁₇×AGL(1,𝔽₇), D₁₇×#11716325, D₁₇×#11716326, …
maximal quotient of	C₃×D₇×C₁₉×D₁₇, C₁₉×D₁₇×D₂₁, D₇×C₁₉×D₅₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9044, 17);