Finite Group Databasebeta

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C₇×D₉×C₇₁ #22582117

order	8946
isoclinism	isoclinic class of D₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₇₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×D₉×C₇₁
unambiguous semidirect product	C₉⋊(C₂×C₇×C₇₁)

Splittings

Fitting, Hall	C₇×C₉×C₇₁ ⋊ C₂
derived, Sylow	C₉ ⋊ C₂×C₇×C₇₁
Hall	C₉×C₇₁ ⋊ C₂×C₇
Hall	C₇×C₉ ⋊ C₂×C₇₁

Subgroups

	subgroup	G/H
center, hypercenter	C₇×C₇₁	D₉
commutator, hypocenter	C₉	C₂×C₇×C₇₁
Frattini	C₃	D₃×C₇×C₇₁
Fitting	C₇×C₉×C₇₁	C₂
socle	C₃×C₇×C₇₁	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₇×C₇₁

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2982 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₇×D₉×D₇₁, D₇×D₉×C₇₁, D₉×D₄₉₇, …
maximal normal subgroup of	C₇×D₉×D₇₁, D₇×D₉×C₇₁, D₉×D₄₉₇, …
maximal quotient of	C₇×Dic₉×C₇₁, C₂×C₇×D₉×C₇₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8946, 7);