Finite Group Databasebeta

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C₂×C₉×D₂₂₁ #22547376

order	7956
isoclinism	isoclinic class of D₂₂₁
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₉×D₂₂₁
unambiguous semidirect product	(C₂×C₁₇)⋊(C₉×D₁₃)

Splittings

Fitting	C₂×C₉×C₁₃×C₁₇ ⋊ C₂
derived, Hall	C₁₃×C₁₇ ⋊ C₂²×C₉
Hall	C₉×C₁₃×C₁₇ ⋊ C₂²
Hall	C₉×C₁₇ ⋊ C₂×D₁₃
Hall	C₉×C₁₃ ⋊ C₂×D₁₇
Sylow	C₁₇ ⋊ C₂×C₉×D₁₃
Sylow	C₁₃ ⋊ C₂×C₉×D₁₇

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₉	D₂₂₁
commutator, hypocenter	C₁₃×C₁₇	C₂²×C₉
Frattini	C₃	C₂×C₃×D₂₂₁
Fitting	C₂×C₉×C₁₃×C₁₇	C₂
socle	C₂×C₃×C₁₃×C₁₇	C₂×C₃
LCS	G ▷ C₁₃×C₁₇
UCS	C₁ ◁ C₂×C₉

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2016 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7956, 48);