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C₁₉×D₁₇₁ #20266595

order	6498
isoclinism	isoclinic class of D₁₇₁
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₉×D₁₇₁
unambiguous semidirect product	C₉⋊(C₁₉×D₁₉)
unambiguous semidirect product	C₁₉⋊(D₉×C₁₉)

Splittings

Fitting, Hall	C₉×C₁₉² ⋊ C₂
derived	C₉×C₁₉ ⋊ C₂×C₁₉
Sylow	C₁₉² ⋊ D₉
Sylow	C₉ ⋊ C₁₉×D₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₁₉	D₁₇₁
commutator, hypocenter	C₉×C₁₉	C₂×C₁₉
Frattini	C₃	C₁₉×D₅₇
Fitting	C₉×C₁₉²	C₂
socle	C₃×C₁₉²	D₃
LCS	G ▷ C₉×C₁₉
UCS	C₁ ◁ C₁₉

51 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1653 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₉×C₁₉×D₁₉, D₁₉×D₁₇₁, D₁₇₁⋊D₁₉, …
maximal normal subgroup of	D₉×C₁₉×D₁₉, D₁₉×D₁₇₁, D₁₇₁⋊D₁₉, …
maximal quotient of	C₁₉×Dic₁₇₁, C₂×C₁₉×D₁₇₁, C₁₉×D₈₅₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6498, 34);