Finite Group Databasebeta

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C₂×C₁₉×C₅²⋊C₉ #22555514

order	8550
isoclinism	isoclinic class of C₅²⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₉ · Schur multiplier (H₂) = C₅

Aliases

direct product	C₂×C₁₉×C₅²⋊C₉
unambiguous semidirect product	(C₂×C₅²)⋊(C₉×C₁₉)

Splittings

derived, Sylow	C₅² ⋊ C₂×C₉×C₁₉
Hall	C₂×C₅²×C₁₉ ⋊ C₉
Hall	C₅²×C₁₉ ⋊ C₂×C₉
Hall	C₂×C₅² ⋊ C₉×C₁₉

Subgroups

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

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1254 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₉×#11744607, C₁₉⋊#11744607, C₁₉×#1039⋊C₉, …
maximal normal subgroup of	C₁₉×#11744607, C₁₉⋊#11744607, C₁₉×#1039⋊C₉, …
maximal quotient of	C₄×C₁₉×C₅²⋊C₉, C₂²×C₁₉×C₅²⋊C₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8550, 52);