Finite Group Databasebeta

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C₃²×C₁₉×D₂₅ #22555489

order	8550
isoclinism	isoclinic class of D₂₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₃²×C₁₉ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃²×C₁₉×D₂₅
unambiguous semidirect product	C₂₅⋊(C₂×C₃²×C₁₉)

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₃²×C₁₉	D₂₅
commutator, hypocenter	C₂₅	C₂×C₃²×C₁₉
Frattini	C₅	C₃²×D₅×C₁₉
Fitting	C₃²×C₁₉×C₂₅	C₂
socle	C₃²×C₅×C₁₉	D₅
LCS	G ▷ C₂₅
UCS	C₁ ◁ C₃²×C₁₉

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2394 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃²×C₁₉×#1035, C₃²×C₁₉⋊#1035, C₃²×D₁₉×D₂₅, …
maximal normal subgroup of	C₃²×C₁₉×#1035, C₃²×C₁₉⋊#1035, C₃²×D₁₉×D₂₅, …
maximal quotient of	C₃²×C₁₉×Dic₂₅, C₂×C₃²×C₁₉×D₂₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8550, 27);