Finite Group Databasebeta

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C₂×C₉×D₃₂₉ #26044883

order	11844
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₉×D₃₂₉
unambiguous semidirect product	(C₂×C₄₇)⋊(C₉×D₇)

Splittings

Fitting	C₂×C₇×C₉×C₄₇ ⋊ C₂
derived, Hall	C₇×C₄₇ ⋊ C₂²×C₉
Hall	C₇×C₉×C₄₇ ⋊ C₂²
Hall	C₉×C₄₇ ⋊ C₂×D₇
Hall	C₇×C₉ ⋊ C₂×D₄₇
Sylow	C₄₇ ⋊ C₂×C₉×D₇
Sylow	C₇ ⋊ C₂×C₉×D₄₇

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₉	D₃₂₉
commutator, hypocenter	C₇×C₄₇	C₂²×C₉
Frattini	C₃	C₂×C₃×D₃₂₉
Fitting	C₂×C₇×C₉×C₄₇	C₂
socle	C₂×C₃×C₇×C₄₇	C₂×C₃
prime radical	C₂×C₃×D₃₂₉	C₃
cosocle	C₃×C₇×C₄₇	C₂²×C₃
LCS	G ▷ C₇×C₄₇
UCS	C₁ ◁ C₂×C₉

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2988 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11844, 30);