Finite Group Databasebeta

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C₉×D₇×C₆₇ #22554720

order	8442
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₆₇ · Schur multiplier (H₂) = C₁

Aliases

C₉×D₇×C₆₇

Splittings

Fitting, Hall	C₇×C₉×C₆₇ ⋊ C₂
derived, Sylow	C₇ ⋊ C₂×C₉×C₆₇
Hall	C₇×C₆₇ ⋊ C₂×C₉
Hall	C₇×C₉ ⋊ C₂×C₆₇

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₆₇	D₇
commutator, hypocenter	C₇	C₂×C₉×C₆₇
Frattini	C₃	C₃×D₇×C₆₇
Fitting	C₇×C₉×C₆₇	C₂
socle	C₃×C₇×C₆₇	C₂×C₃
LCS	G ▷ C₇
UCS	C₁ ◁ C₉×C₆₇

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3015 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₇×D₆₇, D₇×D₉×C₆₇, D₇×D₆₀₃, …
maximal normal subgroup of	C₉×D₇×D₆₇, D₇×D₉×C₆₇, D₇×D₆₀₃, …
maximal quotient of	C₉×Dic₇×C₆₇, C₂×C₉×D₇×C₆₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8442, 7);