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C₃×D₃×C₁₉×C₂₅ #22555491

order	8550
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₁₉×C₂₅ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×D₃×C₁₉×C₂₅
unambiguous semidirect product	C₃⋊(C₂×C₃×C₁₉×C₂₅)

Splittings

Fitting, Hall	C₃²×C₁₉×C₂₅ ⋊ C₂
derived	C₃ ⋊ C₂×C₃×C₁₉×C₂₅
Hall	C₃²×C₂₅ ⋊ C₂×C₁₉
Hall	C₃²×C₁₉ ⋊ C₂×C₂₅
Sylow	C₃² ⋊ C₂×C₁₉×C₂₅

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₉×C₂₅	D₃
commutator, hypocenter	C₃	C₂×C₃×C₁₉×C₂₅
Frattini	C₅	C₃×C₅×D₃×C₁₉
Fitting	C₃²×C₁₉×C₂₅	C₂
socle	C₃²×C₅×C₁₉	C₂×C₅
LCS	G ▷ C₃
UCS	C₁ ◁ C₃×C₁₉×C₂₅

54 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4275 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×D₃×C₂₅×D₁₉, C₃×D₃×C₁₉×D₂₅, C₃×D₃×D₄₇₅, …
maximal normal subgroup of	C₃×D₃×C₂₅×D₁₉, C₃×D₃×C₁₉×D₂₅, C₃×D₃×D₄₇₅, …
maximal quotient of	C₃×Dic₃×C₁₉×C₂₅, C₂×C₃×D₃×C₁₉×C₂₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8550, 29);