Finite Group Databasebeta

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C₂×C₉×D₇×C₄₇ #26044882

order	11844
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉×C₄₇ · Schur multiplier (H₂) = C₂

Aliases

C₂×C₉×D₇×C₄₇

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₉×C₄₇	D₇
commutator, hypocenter	C₇	C₂²×C₉×C₄₇
Frattini	C₃	C₂×C₃×D₇×C₄₇
Fitting	C₂×C₇×C₉×C₄₇	C₂
socle	C₂×C₃×C₇×C₄₇	C₂×C₃
prime radical	C₂×C₃×D₇×C₄₇	C₃
cosocle	C₃×C₇	C₂²×C₃×C₄₇
LCS	G ▷ C₇
UCS	C₁ ◁ C₂×C₉×C₄₇

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4230 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11844, 29);