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C₂×D₃₁×C₅²⋊C₉ #42124534

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

Aliases

C₂×D₃₁×C₅²⋊C₉

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃	D₃₁×C₅²⋊C₃
commutator, hypocenter	C₅²×C₃₁	C₂²×C₉
Frattini	C₃	C₂×D₃₁×C₅²⋊C₃
Fitting, socle	C₂×C₃×C₅²×C₃₁	C₂×C₃
prime radical	C₂×C₃×C₅²×D₃₁	C₃
cosocle	C₃×C₅²×C₃₁	C₂²×C₃
LCS	G ▷ C₅²×C₃₁
UCS	C₁ ◁ C₂×C₃

100 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1122 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 281);