Finite Group Databasebeta

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C₇×C₁₉×D₃₅ #22605016

order	9310
isoclinism	isoclinic class of D₃₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×C₁₉×D₃₅
unambiguous semidirect product	C₅⋊(C₇×D₇×C₁₉)
unambiguous semidirect product	C₇⋊(C₇×D₅×C₁₉)

Splittings

Fitting, socle, Hall	C₅×C₇²×C₁₉ ⋊ C₂
derived	C₅×C₇ ⋊ C₂×C₇×C₁₉
Hall	C₇²×C₁₉ ⋊ D₅
Hall	C₅×C₇² ⋊ C₂×C₁₉
Hall	C₅×C₁₉ ⋊ C₇×D₇
Sylow	C₇² ⋊ D₅×C₁₉
Sylow	C₅ ⋊ C₇×D₇×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₇×C₁₉	D₃₅
commutator, hypocenter	C₅×C₇	C₂×C₇×C₁₉
Frattini	C₁	G
Fitting, socle	C₅×C₇²×C₁₉	C₂
LCS	G ▷ C₅×C₇
UCS	C₁ ◁ C₇×C₁₉

44 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2527 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₇×D₁₉×D₃₅, C₇×D₅×D₇×C₁₉, C₇×D₃₅⋊D₁₉, …
maximal normal subgroup of	C₇×D₁₉×D₃₅, C₇×D₅×D₇×C₁₉, C₇×D₃₅⋊D₁₉, …
maximal quotient of	C₇×C₁₉×Dic₃₅, C₂×C₇×C₁₉×D₃₅, C₃×C₇×C₁₉×D₃₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9310, 17);