Finite Group Databasebeta

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C₃₁×C₂²⋊(C₅²⋊C₉) #42124576

order	27900
automorphism	?
homology	Abelianization (H₁) = C₉×C₃₁ · Schur multiplier (H₂) = C₂×C₅

Aliases

direct product	C₃₁×C₂²⋊(C₅²⋊C₉)
unambiguous semidirect product	C₂²⋊(C₃₁×C₅²⋊C₉)
unambiguous semidirect product	C₅²⋊(C₃₁×C₂²⋊C₉)

Splittings

derived, Hall	C₂²×C₅² ⋊ C₉×C₃₁
Hall	C₂²×C₅²×C₃₁ ⋊ C₉
Hall	C₅²×C₃₁ ⋊ C₂²⋊C₉
Hall	C₂²×C₃₁ ⋊ C₅²⋊C₉
Sylow	C₅² ⋊ C₃₁×C₂²⋊C₉
Sylow	C₂² ⋊ C₃₁×C₅²⋊C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₃₁	C₂²⋊(C₅²⋊C₃)
commutator, hypocenter	C₂²×C₅²	C₉×C₃₁
Frattini	C₃	C₃₁×C₂²⋊(C₅²⋊C₃)
Fitting, socle, prime radical	C₂²×C₃×C₅²×C₃₁	C₃
cosocle	C₂²×C₃×C₅²	C₃×C₃₁
LCS	G ▷ C₂²×C₅²
UCS	C₁ ◁ C₃×C₃₁

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3348 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 323);