Finite Group Databasebeta

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C₂×C₅×C₉×D₄₉ #22578799

order	8820
isoclinism	isoclinic class of D₄₉
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅×C₉ · Schur multiplier (H₂) = C₂

Aliases

C₂×C₅×C₉×D₄₉

Splittings

Fitting	C₂×C₅×C₉×C₄₉ ⋊ C₂
derived, Sylow	C₄₉ ⋊ C₂²×C₅×C₉
Hall	C₅×C₉×C₄₉ ⋊ C₂²
Hall	C₉×C₄₉ ⋊ C₂²×C₅
Hall	C₅×C₄₉ ⋊ C₂²×C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₅×C₉	D₄₉
commutator, hypocenter	C₄₉	C₂²×C₅×C₉
Frattini	C₃×C₇	C₂×C₃×C₅×D₇
Fitting	C₂×C₅×C₉×C₄₉	C₂
socle	C₂×C₃×C₅×C₇	C₃×D₇
LCS	G ▷ C₄₉
UCS	C₁ ◁ C₂×C₅×C₉

90 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2340 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8820, 34);