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C₅²×C₃⋊D₃×C₁₉ #22555587

order	8550
isoclinism	isoclinic class of C₃⋊D₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₅²×C₁₉ · Schur multiplier (H₂) = C₃×C₅

Aliases

direct product	C₅²×C₃⋊D₃×C₁₉
unambiguous semidirect product	C₃⋊(C₅²×D₃×C₁₉)

Splittings

Fitting, socle, Hall	C₃²×C₅²×C₁₉ ⋊ C₂
derived, Sylow	C₃² ⋊ C₂×C₅²×C₁₉
Hall	C₃²×C₅² ⋊ C₂×C₁₉
Hall	C₃²×C₁₉ ⋊ C₂×C₅²

Subgroups

	subgroup	G/H
center, hypercenter	C₅²×C₁₉	C₃⋊D₃
commutator, hypocenter	C₃²	C₂×C₅²×C₁₉
Frattini	C₁	G
Fitting, socle	C₃²×C₅²×C₁₉	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₅²×C₁₉

192 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2850 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅²×C₃⋊D₃×D₁₉, C₅×D₅×C₃⋊D₃×C₁₉, C₅×C₃⋊D₃×D₉₅, …
maximal normal subgroup of	C₅²×C₃⋊D₃×D₁₉, C₅×D₅×C₃⋊D₃×C₁₉, C₅×C₃⋊D₃×D₉₅, …
maximal quotient of	C₅²×C₁₉×C₃⋊Dic₃, C₂×C₅²×C₃⋊D₃×C₁₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8550, 125);