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C₅²×D₁₇₁ #22555522

order	8550
isoclinism	isoclinic class of D₁₇₁
automorphism	?
homology	Abelianization (H₁) = C₂×C₅² · Schur multiplier (H₂) = C₅

Aliases

direct product	C₅²×D₁₇₁
unambiguous semidirect product	C₉⋊(C₅²×D₁₉)
unambiguous semidirect product	C₁₉⋊(C₅²×D₉)

Splittings

Fitting, Hall	C₅²×C₉×C₁₉ ⋊ C₂
derived, Hall	C₉×C₁₉ ⋊ C₂×C₅²
Hall	C₅²×C₁₉ ⋊ D₉
Hall	C₅²×C₉ ⋊ D₁₉
Sylow	C₁₉ ⋊ C₅²×D₉
Sylow	C₉ ⋊ C₅²×D₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₅²	D₁₇₁
commutator, hypocenter	C₉×C₁₉	C₂×C₅²
Frattini	C₃	C₅²×D₅₇
Fitting	C₅²×C₉×C₁₉	C₂
socle	C₃×C₅²×C₁₉	D₃
LCS	G ▷ C₉×C₁₉
UCS	C₁ ◁ C₅²

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2175 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅²×D₉×D₁₉, C₅×D₅×D₁₇₁, C₅×D₄₅⋊D₁₉, …
maximal normal subgroup of	C₅²×D₉×D₁₉, C₅×D₅×D₁₇₁, C₅×D₄₅⋊D₁₉, …
maximal quotient of	C₅²×Dic₁₇₁, C₂×C₅²×D₁₇₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8550, 60);