Finite Group Databasebeta

← Prev (#22582115) Next (#22582117) →

C₉×D₄₉₇ #22582116

order	8946
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×D₄₉₇
unambiguous semidirect product	C₇₁⋊(C₉×D₇)

Splittings

Fitting, Hall	C₇×C₉×C₇₁ ⋊ C₂
derived, Hall	C₇×C₇₁ ⋊ C₂×C₉
Hall	C₉×C₇₁ ⋊ D₇
Sylow	C₇₁ ⋊ C₉×D₇
Hall	C₇×C₉ ⋊ D₇₁
Sylow	C₇ ⋊ C₉×D₇₁

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₄₉₇
commutator, hypocenter	C₇×C₇₁	C₂×C₉
Frattini	C₃	C₃×D₄₉₇
Fitting	C₇×C₉×C₇₁	C₂
socle	C₃×C₇×C₇₁	C₂×C₃
LCS	G ▷ C₇×C₇₁
UCS	C₁ ◁ C₉

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2250 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₇×D₇₁, D₉×D₄₉₇, D₆₃⋊D₇₁, …
maximal normal subgroup of	C₉×D₇×D₇₁, D₉×D₄₉₇, D₆₃⋊D₇₁, …
maximal quotient of	C₉×Dic₄₉₇, C₂×C₉×D₄₉₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8946, 6);