Finite Group Databasebeta

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C₂×C₉×C₅⋊D₁₅₅ #42124588

order	27900
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂×C₅

Aliases

direct product	C₂×C₉×C₅⋊D₁₅₅
unambiguous semidirect product	(C₂×C₅)⋊(C₉×D₁₅₅)

Splittings

Fitting	C₂×C₅²×C₉×C₃₁ ⋊ C₂
derived, Hall	C₅²×C₃₁ ⋊ C₂²×C₉
Hall	C₅²×C₉×C₃₁ ⋊ C₂²
Hall	C₉×C₃₁ ⋊ C₂×C₅⋊D₅
Hall	C₅²×C₉ ⋊ C₂×D₃₁
Sylow	C₃₁ ⋊ C₂×C₉×C₅⋊D₅
Sylow	C₅² ⋊ C₂×C₉×D₃₁

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₉	C₅⋊D₁₅₅
commutator, hypocenter	C₅²×C₃₁	C₂²×C₉
Frattini	C₃	C₂×C₃×C₅⋊D₁₅₅
Fitting	C₂×C₅²×C₉×C₃₁	C₂
socle	C₂×C₃×C₅²×C₃₁	C₂×C₃
prime radical	C₂×C₃×C₅⋊D₁₅₅	C₃
cosocle	C₃×C₅²×C₃₁	C₂²×C₃
LCS	G ▷ C₅²×C₃₁
UCS	C₁ ◁ C₂×C₉

240 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7002 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 335);