Finite Group Databasebeta

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C₅×C₇×D₇×C₁₉ #22605010

order	9310
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₇×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

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

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₅×C₇×C₁₉	D₇
commutator, hypocenter	C₇	C₂×C₅×C₇×C₁₉
Frattini	C₁	G
Fitting, socle	C₅×C₇²×C₁₉	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₅×C₇×C₁₉

44 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3325 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅×C₇×D₇×D₁₉, C₅×D₇²×C₁₉, C₅×D₇×D₁₃₃, …
maximal normal subgroup of	C₅×C₇×D₇×D₁₉, C₅×D₇²×C₁₉, C₅×D₇×D₁₃₃, …
maximal quotient of	C₅×C₇×C₁₉×Dic₇, C₂×C₅×C₇×D₇×C₁₉, C₃×C₅×C₇×D₇×C₁₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9310, 11);